Generates Recalibrated Samples of the Predictive Distribution
Source:R/recalibrate.R
recalibrate.Rd
This function offers recalibration techniques for regression models that assume Gaussian distributions by using the Mean Squared Error (MSE) as the loss function. Based on the work by Torres R. et al. (2024), it supports both local and global recalibration approaches to provide samples from a recalibrated predictive distribution. A detailed algorithm can also be found in Musso C. (2023).
Usage
recalibrate(
yhat_new,
pit_values,
mse,
space_cal = NULL,
space_new = NULL,
type = c("local", "global"),
p_neighbours = 0.1,
epsilon = 0
)
Arguments
- yhat_new
Numeric vector with predicted response values for the new (or test) set.
- pit_values
Numeric vector of Global Probability Integral Transform (PIT) values calculated on the calibration set. We recommend using the PIT_global function.
- mse
Mean Squared Error calculated from the calibration/validation set.
- space_cal
Numeric matrix or data frame representing the covariates/features of the calibration/validation set, or any intermediate representation (like an intermediate layer of a neural network).
- space_new
Similar to space_cal, but for a new set of covariates/features, ensuring they are in the same space as those in space_cal for effective local recalibration.
- type
Character string to choose between 'local' or 'global' calibration.
- p_neighbours
Proportion (0,1] of the calibration dataset to be considered for determining the number of neighbors in the KNN method. Default is set to 0.1. With p_neighbours=1, calibration is global but weighted by distance.
- epsilon
Numeric value for approximation in the K-nearest neighbors (KNN) method. Default is 0, indicating exact distances.
Value
A list containing the calibrated predicted mean and variance, along with samples from the recalibrated predictive distribution and their respective weights calculated using an Epanechnikov kernel over the distances obtained from KNN.
Details
The calibration technique implemented here draws inspiration from Approximate Bayesian Computation and Inverse Transform Theorem, allowing for recalibration either locally or globally. The global method employs a uniform kernel, while the local method employs an Epanechnikov kernel.
It's important to note that the least squares method will only yield a probabilistic interpretation if the output to be modeled follows a normal distribution, and this assumption was used to implement this function.
The local recalibration method is expected to improve the predictive performance of the model, especially when the model is not able to capture the heteroscedasticity of the data. However, there is a trade off between refinement of localization and the Monte Carlo error, which can be controlled by the number of neighbors. That is, when more localized, the recalibration will grasp local changes better, but the Monte Carlo error will increase, because of the reduced number of neighbors.
When p_neighbours=1, recalibration is performed using the entire calibration dataset but with distance-weighted contributions.
References
Torres R, Nott DJ, Sisson SA, Rodrigues T, Reis JG, Rodrigues GS (2024). “Model-Free Local Recalibration of Neural Networks.” arXiv preprint arXiv:2403.05756. doi:10.48550/arXiv.2403.05756 . Musso C (2023). “Recalibration of Gaussian Neural Network Regression Models: The RecalibratiNN Package.” Undergraduate Thesis (Bachelor in Statistics), University of Brasília. Available at: https://bdm.unb.br/handle/10483/38504.
Examples
n <- 1000
split <- 0.8
# Auxiliary functions
mu <- function(x1){
10 + 5*x1^2
}
sigma_v <- function(x1){
30*x1
}
# Generating heteroscedastic data.
x <- runif(n, 1, 10)
y <- rnorm(n, mu(x), sigma_v(x))
# Train set
x_train <- x[1:(n*split)]
y_train <- y[1:(n*split)]
# Calibration/Validation set.
x_cal <- x[(n*split+1):n]
y_cal <- y[(n*split+1):n]
# New observations or the test set.
x_new <- runif(n/5, 1, 10)
# Fitting a simple linear regression, which will not capture the heteroscedasticity
model <- lm(y_train ~ x_train)
y_hat_cal <- predict(model, newdata=data.frame(x_train=x_cal))
MSE_cal <- mean((y_hat_cal - y_cal)^2)
y_hat_new <- predict(model, newdata=data.frame(x_train=x_new))
pit <- PIT_global(ycal=y_cal, yhat= y_hat_cal, mse=MSE_cal)
recalibrate(
space_cal=x_cal,
space_new=x_new,
yhat_new=y_hat_new,
pit_values=pit,
mse= MSE_cal,
type="local")
#> $y_hat_calibrated
#> [1] 485.467895 -12.945198 374.112687 99.840667 107.255488 192.982238
#> [7] 422.951289 391.238172 351.293065 4.129723 280.065034 434.402371
#> [13] 64.604296 104.450484 304.385936 344.586737 134.346132 438.028930
#> [19] 278.531799 274.986644 111.625343 320.901558 458.262613 495.696836
#> [25] 20.682320 437.299183 473.384651 150.185745 4.443241 100.205873
#> [31] 192.126299 194.716654 130.681400 46.166531 105.004336 44.085033
#> [37] 110.633031 350.353674 275.120246 322.352246 29.002925 153.403903
#> [43] 108.161682 49.719058 152.260241 67.588321 21.448095 260.112335
#> [49] 298.553171 382.152651 191.272565 22.345222 436.796545 143.310265
#> [55] 61.647502 219.728100 433.917862 330.559690 379.787519 108.110190
#> [61] 108.215922 40.966430 62.105087 112.125437 106.652615 49.437792
#> [67] 303.499422 20.473107 101.592068 193.056434 486.611514 435.414317
#> [73] 64.659541 42.661794 193.034900 292.629904 65.901085 63.287608
#> [79] 313.333770 151.520106 35.451841 129.364703 125.066741 269.053687
#> [85] 110.856972 114.243187 61.855196 183.729374 123.283913 50.782674
#> [91] 261.815579 153.568949 75.900222 486.395392 300.481164 39.875221
#> [97] 100.887255 121.159823 15.983318 110.648239 129.599288 433.815683
#> [103] 436.160302 191.941070 365.414860 211.399614 36.098345 108.553655
#> [109] 155.637994 314.262629 193.783916 170.101894 108.021861 286.309022
#> [115] 494.770168 488.768369 106.509585 65.928112 123.306027 65.118140
#> [121] 144.783255 127.651786 153.272324 192.461857 110.662687 104.544045
#> [127] 10.614931 117.456182 61.376394 322.918738 108.521269 192.231416
#> [133] 301.751521 40.889026 105.590994 41.942925 151.558910 338.012268
#> [139] 16.358457 63.908481 98.853427 454.540660 495.411083 175.993051
#> [145] 355.460400 65.916285 205.792162 352.950706 156.351172 40.210054
#> [151] 149.317098 346.879845 318.634201 63.795803 129.701003 317.825374
#> [157] 329.322016 62.820430 -11.972407 63.600579 45.283979 148.585610
#> [163] 229.335723 111.514798 236.045059 -9.212537 351.778306 123.006308
#> [169] 83.964664 325.845964 261.758232 307.805937 104.454434 48.238874
#> [175] 55.058180 150.217685 128.657595 354.743841 28.688702 94.990038
#> [181] 300.198916 150.991284 48.014782 268.468015 105.198036 173.650962
#> [187] 169.789496 384.012848 153.846980 130.978847 182.957749 156.793975
#> [193] 459.888329 69.214582 362.375842 119.396870 107.956541 112.015906
#> [199] 471.297311 118.414956
#>
#> $y_var_calibrated
#> [1] 119360.0898 1019.1288 77797.6574 23887.7659 25100.0054 41007.7886
#> [7] 83989.4968 41098.1750 90808.2516 960.0762 72008.0273 108203.6204
#> [13] 11161.8383 17395.2059 37865.4205 61098.2921 64251.3118 83247.3615
#> [19] 71634.4126 60896.4152 19869.9232 92339.7950 118274.3624 120240.0849
#> [25] 2564.2648 83214.5344 79764.7147 15186.9987 957.0551 23802.7062
#> [31] 39084.9286 58612.4939 13441.5971 2686.9671 24800.9927 3158.5561
#> [37] 19225.4584 91151.1724 70212.9493 37881.9359 2857.2983 16233.6932
#> [43] 23694.5412 3619.7737 57953.4047 6385.2766 2162.9993 43294.4655
#> [49] 58689.5888 37161.9272 65438.1814 1245.2108 95044.9311 13118.7810
#> [55] 12761.4127 48846.7939 97818.1513 61592.3891 51330.6790 23558.0291
#> [61] 23787.8110 3258.3806 4801.4921 14332.8389 21941.5968 3595.4050
#> [67] 37848.0267 1697.9967 19346.7382 61902.1578 119444.1988 96521.6797
#> [73] 11144.7482 2217.6845 56128.5650 59923.1328 10641.5958 9077.7831
#> [79] 76630.7251 15639.7472 3405.9680 13193.8704 13329.3968 63914.6491
#> [85] 13746.2929 62764.1277 4772.1256 45760.9935 12921.8956 3727.8911
#> [91] 42935.1200 66059.7467 15912.2272 119428.0233 58234.0179 3294.2262
#> [97] 19184.9741 13835.7529 990.6550 25407.4605 13409.3861 107067.4983
#> [103] 111822.3252 38802.9034 39861.0964 48750.4996 3392.6002 24155.3771
#> [109] 23198.6621 62828.4824 60704.2616 66920.9142 23460.8465 71502.0843
#> [115] 120148.8362 119612.7716 16501.0128 10623.3353 12902.0465 9983.4622
#> [121] 15332.2517 13503.1147 16166.7189 39685.2011 19232.7939 23599.7608
#> [127] 970.4899 13898.9787 4720.3448 97377.2875 25274.9384 42246.4633
#> [133] 37874.9613 2256.0994 23225.9554 3207.1834 15652.2273 60811.2527
#> [139] 991.4332 5579.0438 24077.7023 118209.1226 120211.7129 30593.2936
#> [145] 41228.2094 10631.4610 48661.1325 41896.1834 23662.5683 2208.6334
#> [151] 57935.4338 93273.7577 38094.3786 5060.5969 13501.1628 63206.2808
#> [157] 39614.4933 4896.3378 1017.0526 7943.7643 3091.0144 15035.7063
#> [163] 48477.3841 19449.6741 47772.6152 1010.9162 42390.5989 13688.4652
#> [169] 16923.0631 38628.9596 42946.8085 60232.0458 21189.4741 2999.8419
#> [175] 4065.2487 15133.6284 57986.7330 87138.0168 2765.6715 18106.0839
#> [181] 58303.2213 65771.8960 2992.7290 41771.3043 22579.1226 50131.9558
#> [187] 66917.8578 37871.6498 57764.6695 13001.1801 46250.1565 23834.7593
#> [193] 84384.2339 7025.2360 82416.8344 62338.7452 16109.4379 19689.0622
#> [199] 118608.3660 13874.3046
#>
#> $y_samples_calibrated_wt
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 281.69009434 480.417205 951.423407 963.8181228 762.280338
#> [2,] -19.00103157 -3.124400 -42.576221 47.5400698 47.540070
#> [3,] 751.70733126 280.658313 208.067652 441.4708455 418.042687
#> [4,] 88.74976840 -74.447701 142.157975 296.4061202 149.890943
#> [5,] 193.61849290 93.241856 93.241856 121.8847999 93.241856
#> [6,] 277.65952429 93.182082 39.796006 438.8239074 84.545371
#> [7,] 580.92104539 448.524693 768.993039 674.6573471 927.537007
#> [8,] 255.56848174 328.147030 399.095358 70.5987443 176.449612
#> [9,] 508.66890307 -305.656356 128.800889 744.4969420 200.857263
#> [10,] 5.15341235 30.925609 14.727841 -24.7239806 -0.883668
#> [11,] -8.06065955 49.178557 371.421082 49.1785573 49.178557
#> [12,] 691.82079358 944.700454 743.162668 -272.0197999 -8.221401
#> [13,] 120.59577453 61.721617 167.564204 77.6699202 -63.569998
#> [14,] -19.16582130 -42.586542 148.915674 -42.5865421 -179.182711
#> [15,] 667.24009920 371.761339 493.148332 425.1770705 371.761339
#> [16,] 732.93826777 622.908477 24.713008 242.1712235 399.663740
#> [17,] -242.93039766 153.573835 18.309057 -249.3096422 126.089234
#> [18,] 728.33685838 145.402761 427.434170 145.4027614 583.258682
#> [19,] 563.78731678 309.498031 110.032996 48.8064963 48.806496
#> [20,] 96.22602261 549.980344 393.410419 -48.0988307 650.948525
#> [21,] 89.94024525 89.940245 48.124668 265.9023332 143.636091
#> [22,] 840.54036727 593.645310 556.215868 384.3669393 295.343389
#> [23,] 223.73217376 824.077744 940.200970 -0.3261689 751.057901
#> [24,] 624.70288770 399.018721 623.838446 -246.2658454 882.853244
#> [25,] -49.30633292 62.499737 -3.334692 -49.3063329 80.725897
#> [26,] 450.71487865 771.183225 -289.201933 321.0066143 581.879093
#> [27,] 935.57408428 530.970217 408.093652 408.0936516 330.213372
#> [28,] 106.84473220 25.793680 395.768551 395.7685506 196.479070
#> [29,] 5.52465231 -38.014479 -24.352741 65.7635502 -38.014479
#> [30,] 188.90180373 -71.228736 -74.672302 66.5776349 188.901804
#> [31,] 370.23564509 16.332765 276.099999 276.0999991 267.932532
#> [32,] 603.30985717 559.030786 603.309857 386.3033234 603.309857
#> [33,] 386.60555648 33.937915 406.130862 406.1308625 177.131369
#> [34,] -10.85521504 72.619379 64.457908 33.7082732 33.708273
#> [35,] 234.29837183 145.953620 145.953620 382.0042703 -70.222559
#> [36,] 101.16206680 20.283015 58.244214 101.1620668 139.405981
#> [37,] 91.79949038 91.799490 145.495336 267.7615783 147.805916
#> [38,] 128.58205025 434.041618 385.573500 -11.9839753 200.638425
#> [39,] 108.10378071 825.293234 108.103781 369.1198063 46.877281
#> [40,] 497.85211086 497.852111 376.465117 298.0887735 203.872115
#> [41,] 0.78543043 79.766823 25.340344 79.7668234 79.766823
#> [42,] 351.36617579 181.508054 23.811034 351.3661758 9.396261
#> [43,] 86.55797001 101.087004 242.839963 162.2281785 101.087004
#> [44,] -19.48842039 26.540975 84.402771 85.3526772 36.362971
#> [45,] 462.64753072 337.676918 -19.233197 169.0521446 334.220899
#> [46,] 205.98971801 61.092112 -53.549871 29.3782554 151.759777
#> [47,] -1.72253611 32.169418 25.892512 32.1694179 76.302327
#> [48,] 346.07757399 413.421282 346.077574 214.3895706 -173.247163
#> [49,] -178.13703124 290.924242 290.924242 -178.1370312 258.258530
#> [50,] 381.81930302 382.224147 249.820686 325.1153873 317.687372
#> [51,] 608.82839753 174.905840 608.828398 113.2087756 113.208776
#> [52,] 20.16937597 49.263345 23.356595 67.4895043 17.079689
#> [53,] 689.43887079 942.318531 783.774563 740.7807457 595.702569
#> [54,] 167.46970998 6.518058 81.299022 220.1462173 41.710512
#> [55,] -92.16049250 124.015686 99.250423 -92.5899898 94.503404
#> [56,] 127.81232624 -6.168586 127.812326 407.7408802 -220.766721
#> [57,] -10.12208748 689.920107 689.920107 741.2619821 689.920107
#> [58,] 404.92908255 275.646619 273.321196 -195.7400773 30.383195
#> [59,] 334.06704596 423.285929 724.450333 334.0670460 724.450333
#> [60,] 79.57274681 101.520279 86.991245 79.5727468 -58.233624
#> [61,] 86.28303862 154.220280 154.220280 -58.9418306 161.953247
#> [62,] -27.56163069 -27.561631 86.778745 54.0474372 -44.123518
#> [63,] 49.48096787 87.875125 -61.468786 35.1784280 12.562002
#> [64,] 160.28412094 185.883267 199.826179 156.4904057 185.883267
#> [65,] 375.07667186 227.370773 -77.579655 18.4443123 18.444312
#> [66,] 38.16240310 -19.641391 10.622451 -19.6413908 1.725113
#> [67,] 501.83753884 364.464391 144.991206 492.8910222 666.982789
#> [68,] 36.66967867 7.511300 52.976702 27.0699527 52.976702
#> [69,] 222.89175723 222.891757 -78.615105 134.5470050 288.795150
#> [70,] 228.46908953 172.037325 -71.652817 -10.3951999 -258.679371
#> [71,] 964.49784999 -252.222404 618.746329 711.6181899 359.137138
#> [72,] 942.56714990 468.556584 741.029365 459.1662319 213.703638
#> [73,] -95.62809488 59.627460 167.516514 222.5198354 95.782821
#> [74,] 52.12856325 76.230405 76.230405 119.5743703 37.319299
#> [75,] 106.63222454 385.245313 452.274050 235.9940301 235.994030
#> [76,] 354.33102967 577.343795 142.465349 390.4994004 648.037506
#> [77,] 93.98907360 73.827644 -97.851339 -38.8135005 93.989074
#> [78,] -46.54623020 66.094914 81.509325 68.0957528 -73.144165
#> [79,] -26.47253409 835.041773 56.625820 415.0367155 378.868345
#> [80,] 396.49835344 76.437979 44.133748 180.2753814 182.627821
#> [81,] 91.36185164 9.106781 89.985833 18.4161846 74.082325
#> [82,] 236.37231948 51.984191 185.739123 -47.1270164 80.535560
#> [83,] 84.90199099 56.350622 164.351622 -42.7605856 159.955277
#> [84,] 653.29772895 552.329548 147.725572 265.3745497 359.591252
#> [85,] 111.81937933 -9.984769 22.996794 196.2469594 130.997794
#> [86,] -30.59482553 91.662349 326.315290 385.6773332 124.978800
#> [87,] 34.87793181 -88.367217 94.786194 50.8718621 143.540366
#> [88,] 444.06563432 227.785615 -83.569270 -22.3116522 444.065634
#> [89,] 160.44183551 24.300202 184.102337 -39.9215875 162.794275
#> [90,] -71.62571752 61.777823 84.929758 2.4050708 2.405071
#> [91,] 353.61209206 282.275386 360.651730 289.7034016 214.408700
#> [92,] 120.80008224 -254.598794 238.928910 -248.2195499 616.419704
#> [93,] -57.55351356 362.662910 221.536684 221.5366842 221.536684
#> [94,] 270.13007501 711.488461 235.504609 370.8622798 835.850180
#> [95,] 457.38469016 292.322282 574.560615 47.0588573 90.531824
#> [96,] 133.06490291 -28.756026 13.941936 23.2513403 -45.317914
#> [97,] 180.80318888 -82.770917 80.426552 104.3224773 87.216676
#> [98,] 27.24746555 164.657979 164.657979 162.3473981 116.070051
#> [99,] -3.29162639 -22.723180 -3.291626 2.4176004 38.455701
#> [100,] 30.51833630 387.150696 97.691838 75.7443060 305.348190
#> [101,] 62.26823189 69.278892 401.853913 8.4086146 168.458074
#> [102,] -8.48787877 372.998288 262.305948 215.5704639 372.998288
#> [103,] -270.40973349 946.310520 693.430860 264.1824916 946.310520
#> [104,] 91.33192006 16.042128 16.042128 586.9515420 -29.403541
#> [105,] 413.86092569 220.993308 321.377065 378.4858252 220.993308
#> [106,] 406.98741867 322.307592 -179.681027 649.0504474 474.958681
#> [107,] 92.14273878 74.863213 53.089026 37.7162594 129.010634
#> [108,] 241.61890301 99.865944 -196.484128 -59.8879595 153.274151
#> [109,] 257.45208950 249.284622 407.923336 148.4733852 361.558486
#> [110,] 130.77538198 448.477903 448.477903 636.3475388 283.415494
#> [111,] 227.20882660 109.079998 -72.913080 364.5514152 -1.081001
#> [112,] 395.23668538 178.320661 116.623597 178.3206614 612.243219
#> [113,] -57.62769004 163.267388 133.874526 87.5971792 -57.627690
#> [114,] 50.46659411 828.882547 -6.772623 828.8825471 828.882547
#> [115,] 486.40377895 398.369009 969.804697 376.2988556 240.941185
#> [116,] 620.07293913 619.208498 -250.895794 491.8138942 236.960947
#> [117,] 189.16727439 151.017041 -177.081343 55.5056187 194.352814
#> [118,] 73.74399786 213.595116 73.743998 73.7439979 -38.897146
#> [119,] 117.28930277 167.265066 162.868721 162.8687211 24.071612
#> [120,] 217.35493124 68.765096 -68.782593 40.7434686 85.870898
#> [121,] 71.97307881 258.946395 39.365812 411.5587596 78.983739
#> [122,] 50.89033934 18.586108 -2.969278 237.8636551 -2.969278
#> [123,] 397.54889509 27.574024 138.098944 183.6783627 397.548895
#> [124,] 370.79353691 -89.812630 38.794373 268.4904238 83.543738
#> [125,] 188.81136268 49.964167 183.625823 255.4802359 267.741832
#> [126,] -55.13013433 394.082627 138.682663 90.0947349 158.031976
#> [127,] 21.78278922 -7.375590 33.960744 0.5810251 -17.669032
#> [128,] 114.69546198 25.872877 114.695462 204.3085820 190.365671
#> [129,] 71.06574057 -9.673516 197.201789 142.9718477 46.177875
#> [130,] 597.20624996 8.446137 183.893463 844.1013072 183.893463
#> [131,] 122.24309984 -69.597313 26.426654 -69.1678156 26.426654
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#> [138,] 272.107715 437.170123 437.170123 735.0695498 433.90514540
#> [139,] 16.590510 42.471962 -13.286883 80.6500288 42.47196244
#> [140,] 195.176380 -57.315882 -4.651598 41.3777975 55.32526180
#> [141,] 23.032248 379.664608 231.958710 190.5823870 297.86210239
#> [142,] 605.081010 257.458926 222.833460 468.2960543 823.17903073
#> [143,] 288.125087 376.747274 882.651952 288.1250873 957.85839955
#> [144,] 360.806541 104.092427 6.903661 28.8073771 6.90366138
#> [145,] 61.014999 389.511613 61.014999 375.5836361 375.26720012
#> [146,] -97.468058 118.708121 220.679872 -38.8597166 93.94285742
#> [147,] 180.450960 207.427981 45.570791 126.5311391 11.93157024
#> [148,] 683.608122 683.608122 518.462872 406.3999158 215.53635950
#> [149,] 363.465571 39.855551 21.495657 409.8304214 -0.40805909
#> [150,] 120.267811 -26.541233 39.388759 39.3887589 31.26256072
#> [151,] 194.454413 333.030755 -20.423341 -193.1823210 308.80629835
#> [152,] 409.589808 848.506680 564.182180 507.4264132 -306.89884535
#> [153,] 505.167884 -158.418340 496.221368 152.1886277 33.72198298
#> [154,] 90.005230 14.692107 -59.338681 68.7168743 200.20090774
#> [155,] 168.619512 14.867613 71.792768 251.7554245 32.47787762
#> [156,] 410.796201 253.708529 36.250313 279.1883151 36.25031344
#> [157,] 431.683192 499.654454 396.538015 508.6009710 232.02443042
#> [158,] 52.049922 38.102458 144.718426 191.9010409 -60.59122181
#> [159,] -17.749953 -18.015076 -25.587596 -17.7499525 -62.84500956
#> [160,] 48.424636 209.270545 23.761744 64.3729391 82.53353014
#> [161,] -25.522704 53.190217 22.440583 87.4161277 60.40178186
#> [162,] 20.376826 105.373000 195.007338 105.3729999 347.93196792
#> [163,] -178.131871 208.877813 128.608021 276.7444996 355.12084325
#> [164,] -183.245789 -183.245789 174.245457 188.1883687 267.11883850
#> [165,] 284.922334 277.494319 348.831025 -177.3820512 14.75827179
#> [166,] 13.254404 -6.140922 -60.041110 -34.4773048 -52.44810325
#> [167,] 373.451075 405.561198 405.561198 405.5611983 214.69764201
#> [168,] 67.402053 285.179718 285.179718 285.1797185 192.30633726
#> [169,] 174.736741 -56.397461 103.003048 282.0164567 74.36010495
#> [170,] 498.680608 507.627124 -155.959100 298.9172703 -155.95910011
#> [171,] 214.386019 134.116227 188.036047 414.0447805 188.03604696
#> [172,] 286.380008 133.739895 568.618341 554.8839463 -185.00668849
#> [173,] 91.724577 84.934454 138.342661 -78.2630152 -78.26301522
#> [174,] 144.791181 -17.029748 64.579319 106.5472661 25.66821392
#> [175,] 87.408712 87.408712 183.345499 -16.4824789 39.36891204
#> [176,] 245.035535 106.582963 415.032087 106.5829627 82.45706607
#> [177,] -235.304547 302.143983 302.143983 128.4879696 -7.70431297
#> [178,] 746.172758 202.533079 275.123740 510.3447195 275.12374040
#> [179,] -46.068761 83.963469 24.457794 83.9634688 61.60474673
#> [180,] 77.100507 -86.096962 -85.667465 130.5087141 -86.09696186
#> [181,] 523.996014 387.868945 264.669797 139.8348936 -178.91169020
#> [182,] 14.193077 83.429687 116.746139 121.9732546 121.97325458
#> [183,] 97.470247 -40.102158 106.706886 25.8278339 17.70163566
#> [184,] 355.025124 291.116434 657.543523 283.6884185 215.82173192
#> [185,] -76.938369 86.259100 293.915452 19.0855980 114.90204353
#> [186,] -224.987809 123.591238 271.727717 145.1839518 343.06442228
#> [187,] 111.451780 372.150313 -164.454905 8.8987186 234.80772460
#> [188,] 527.139153 318.429299 225.473557 325.8573141 225.47355720
#> [189,] 593.657486 463.396922 -138.816866 397.7883523 0.89753698
#> [190,] 167.343858 287.299519 167.343858 155.6925424 118.75592972
#> [191,] 90.258046 60.351190 -21.840704 -270.1248749 283.37219940
#> [192,] 40.687027 -45.022252 211.372418 -45.0222522 0.42341713
#> [193,] 244.155471 -14.528338 591.777555 454.9925987 736.85573146
#> [194,] 200.691650 44.846601 153.509035 76.2549431 22.23017590
#> [195,] -7.215788 205.406612 133.350237 513.2182518 -301.10700680
#> [196,] 193.171449 158.958985 299.903283 -243.9244917 104.65455534
#> [197,] 154.099177 -39.713620 154.099177 16.6886642 105.51124962
#> [198,] 187.445364 182.259824 320.017630 173.5024523 401.82013541
#> [199,] 944.433222 363.322097 262.589892 -259.8923155 755.29015294
#> [200,] 115.019916 204.633036 -166.801121 65.7858408 190.69012497
#> [,199] [,200]
#> [1,] 10.896268 392.382435
#> [2,] -3.124400 -32.282779
#> [3,] 573.867198 418.042687
#> [4,] 74.220734 -74.447701
#> [5,] -66.512047 93.241856
#> [6,] 17.892290 277.659524
#> [7,] 580.921045 522.933139
#> [8,] 529.428868 608.500526
#> [9,] 304.552192 273.447924
#> [10,] -45.978725 69.212931
#> [11,] 110.405057 178.702603
#> [12,] 743.162668 250.462408
#> [13,] 45.956063 75.669081
#> [14,] 148.915674 -19.165821
#> [15,] 502.094849 502.094849
#> [16,] 399.663740 431.773863
#> [17,] 381.560651 -34.711507
#> [18,] 771.330675 525.270776
#> [19,] 580.327392 178.330542
#> [20,] 298.016480 34.999523
#> [21,] -184.462294 111.887778
#> [22,] -20.973940 180.332523
#> [23,] 347.234974 864.994522
#> [24,] 241.590896 365.093696
#> [25,] -54.571657 -2.397219
#> [26,] 427.286720 402.246761
#> [27,] 935.574084 -17.347771
#> [28,] 82.718836 196.479070
#> [29,] 15.099081 65.763550
#> [30,] 117.168111 188.901804
#> [31,] 91.622557 276.099999
#> [32,] 107.690235 237.052041
#> [33,] 406.130862 202.885301
#> [34,] 72.619379 33.708273
#> [35,] 234.298372 300.201765
#> [36,] 58.244214 -38.976835
#> [37,] 113.747023 10.395403
#> [38,] 744.278104 410.613459
#> [39,] -10.361936 307.568816
#> [40,] 506.798628 671.943878
#> [41,] 25.340344 37.525891
#> [42,] 84.681311 84.681311
#> [43,] 242.839963 86.557970
#> [44,] 85.352677 36.362971
#> [45,] -139.566257 394.676269
#> [46,] 29.378255 29.378255
#> [47,] -6.820789 76.302327
#> [48,] 214.389571 214.389571
#> [49,] 47.986241 290.924242
#> [50,] 224.731630 715.498675
#> [51,] 242.570581 74.665208
#> [52,] 9.507169 45.545269
#> [53,] -10.603324 -274.401723
#> [54,] 41.710512 39.125325
#> [55,] -92.589990 81.089832
#> [56,] 13.212757 350.741530
#> [57,] 741.261982 337.439055
#> [58,] 275.646619 437.444050
#> [59,] 493.009506 724.450333
#> [60,] -58.233624 86.991245
#> [61,] -58.941831 -58.941831
#> [62,] -20.836226 84.244439
#> [63,] -61.468786 -61.468786
#> [64,] 194.640639 156.490406
#> [65,] 85.617814 -74.136089
#> [66,] 61.097865 77.038236
#> [67,] 300.555700 389.774583
#> [68,] 27.069953 13.220526
#> [69,] 87.928921 370.597656
#> [70,] 172.037325 -258.679371
#> [71,] 490.487285 952.103134
#> [72,] -10.354705 942.567150
#> [73,] 75.621391 91.035802
#> [74,] 75.280498 75.280498
#> [75,] 282.942200 602.251846
#> [76,] 260.114327 577.343795
#> [77,] 72.136253 89.242055
#> [78,] 111.021607 50.100984
#> [79,] 550.717273 -0.613397
#> [80,] 44.133748 26.523483
#> [81,] 89.985833 36.935372
#> [82,] 80.535560 17.094773
#> [83,] 181.263339 21.461203
#> [84,] 98.575227 298.040262
#> [85,] 158.096726 130.997794
#> [86,] -245.192960 157.690516
#> [87,] 49.180472 143.540366
#> [88,] 98.423809 -11.737190
#> [89,] -39.921587 192.944552
#> [90,] 27.067962 180.866545
#> [91,] 282.275386 346.723753
#> [92,] 148.284682 238.928910
#> [93,] 126.612259 79.994175
#> [94,] 249.152484 618.616601
#> [95,] 47.058857 574.560615
#> [96,] 101.276203 -22.030622
#> [97,] 133.834759 133.834759
#> [98,] 164.657979 205.683171
#> [99,] 2.417600 38.455701
#> [100,] -62.062065 83.162804
#> [101,] 93.404788 189.766136
#> [102,] 229.218339 461.033058
#> [103,] 340.949808 374.874832
#> [104,] 220.693726 82.695209
#> [105,] 410.595948 63.828780
#> [106,] 406.987419 207.328657
#> [107,] -38.075619 90.766720
#> [108,] 32.692442 85.336910
#> [109,] 19.588571 94.873621
#> [110,] 130.775382 255.610285
#> [111,] -259.939634 -1.081001
#> [112,] 612.243219 116.623597
#> [113,] 102.126213 163.267388
#> [114,] -32.631760 50.466594
#> [115,] 882.203533 623.188735
#> [116,] 491.813894 372.318618
#> [117,] 153.327622 189.167274
#> [118,] 59.796534 75.744837
#> [119,] 162.868721 396.264560
#> [120,] 56.509022 -100.792999
#> [121,] 132.583503 192.743973
#> [122,] 50.890339 18.283073
#> [123,] 84.499180 351.184045
#> [124,] 83.543738 437.822274
#> [125,] 91.779745 113.727277
#> [126,] 246.376728 138.682663
#> [127,] 21.782789 34.371737
#> [128,] 199.123042 163.283390
#> [129,] -9.673516 65.717755
#> [130,] 65.685354 183.893463
#> [131,] 93.600156 93.600156
#> [132,] 87.626035 272.572721
#> [133,] 492.342619 292.579282
#> [134,] 110.711577 69.818798
#> [135,] 65.010727 -72.795644
#> [136,] 16.921342 -25.776621
#> [137,] 350.155650 83.470785
#> [138,] 119.467602 269.782292
#> [139,] 42.362707 2.715787
#> [140,] 147.993765 -4.651598
#> [141,] -40.551815 231.958710
#> [142,] 380.261285 750.159187
#> [143,] 376.747274 957.858400
#> [144,] 47.167271 73.556742
#> [145,] 243.268583 684.990373
#> [146,] 213.632546 220.679872
#> [147,] -222.047908 274.667618
#> [148,] 406.399916 59.632748
#> [149,] 21.495657 363.465571
#> [150,] 78.299864 19.488162
#> [151,] 461.457387 591.717951
#> [152,] -306.898845 127.558399
#> [153,] 374.834374 670.313135
#> [154,] 39.354999 193.153582
#> [155,] 32.174842 14.867613
#> [156,] 376.907677 128.873625
#> [157,] 508.600971 205.674459
#> [158,] 198.948367 72.812319
#> [159,] -55.252003 10.039511
#> [160,] 82.533530 -76.866979
#> [161,] 50.269175 14.314385
#> [162,] 178.073846 210.576563
#> [163,] 408.536575 650.599604
#> [164,] 91.156751 320.760635
#> [165,] 183.277661 210.254683
#> [166,] -34.477305 -6.140922
#> [167,] 164.644897 58.794030
#> [168,] 165.224057 165.224057
#> [169,] 216.113064 7.186603
#> [170,] 204.700612 395.564169
#> [171,] -172.623665 289.680720
#> [172,] 133.739895 568.618341
#> [173,] 374.393311 374.393311
#> [174,] 107.923285 17.542016
#> [175,] -16.482479 13.781363
#> [176,] 106.582963 82.457066
#> [177,] 585.055636 -241.683791
#> [178,] -303.980539 202.533079
#> [179,] 39.830560 24.457794
#> [180,] 225.433139 55.152975
#> [181,] 457.537414 523.996014
#> [182,] 290.402152 83.429687
#> [183,] 25.827834 64.738939
#> [184,] -171.187952 135.551940
#> [185,] -73.494803 293.915452
#> [186,] 204.488080 318.839966
#> [187,] 116.678896 372.150313
#> [188,] 415.076197 250.562612
#> [189,] -191.242786 -233.081941
#> [190,] 208.369050 208.369050
#> [191,] 228.256563 387.478595
#> [192,] 211.372418 40.687027
#> [193,] 938.393517 -280.535610
#> [194,] -110.838451 59.149141
#> [195,] 415.381646 749.046291
#> [196,] 158.958985 299.903283
#> [197,] 151.788597 -176.309788
#> [198,] 266.375833 97.832244
#> [199,] 3.906083 262.589892
#> [200,] -8.995123 165.090979
#>
#> $y_samples_calibrated_raw
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 876.2169590 951.423407 281.690094 370.312281 489.807557
#> [2,] 47.5400698 -9.930778 -38.267160 -18.735908 8.782077
#> [3,] -298.4459663 393.002727 136.011278 761.939192 418.042687
#> [4,] 88.7497684 21.576266 296.406120 230.502727 378.208626
#> [5,] 382.7007139 234.994815 71.294324 93.241856 26.068354
#> [6,] 371.7951703 -16.978917 -27.553379 84.545371 269.492057
#> [7,] 522.9331395 322.176295 448.524693 425.096534 768.993039
#> [8,] 385.2557896 70.598744 718.530317 417.365913 529.428868
#> [9,] 304.5521920 565.424670 273.447924 744.496942 128.800889
#> [10,] 5.1534124 14.727841 -6.473923 30.925609 -45.978725
#> [11,] 564.1593778 580.699453 49.178557 371.421082 407.589453
#> [12,] 743.1626685 691.820794 944.700454 250.462408 373.264766
#> [13,] -63.5699979 -95.580404 95.830511 -96.009901 75.669081
#> [14,] 53.4042515 151.226255 178.308536 148.915674 -19.165821
#> [15,] 667.2400992 371.761339 225.518309 199.168337 357.833362
#> [16,] 242.1712235 399.258896 435.038841 732.938268 85.006695
#> [17,] 381.5606513 -242.930398 577.429785 153.573835 244.218063
#> [18,] 324.5139316 525.270776 214.659007 450.862329 583.258682
#> [19,] 563.7873168 580.327392 48.806496 371.049021 407.217392
#> [20,] 52.7530559 295.691057 263.025345 96.226023 -173.370216
#> [21,] -184.4622943 97.358743 -24.445405 173.028952 48.124668
#> [22,] 191.6484604 180.332523 840.540367 4.885197 -20.973940
#> [23,] -0.3261689 223.732174 469.194768 -264.124568 381.159998
#> [24,] 624.7028877 841.936467 376.948567 882.853244 958.059692
#> [25,] 62.4997372 80.725897 21.220221 -54.571657 36.592988
#> [26,] 324.3664812 525.123325 214.511556 450.714879 583.111231
#> [27,] 588.9581224 220.358447 330.213372 935.574084 682.694424
#> [28,] 25.7936798 82.718836 181.898018 262.681492 21.848559
#> [29,] 5.5246523 15.099081 -6.102683 31.296848 -45.607485
#> [30,] 88.5251673 21.351665 296.181519 230.278126 377.984025
#> [31,] 370.2356451 -18.538442 -29.112904 82.985846 267.932532
#> [32,] 603.3098572 237.052041 107.690235 453.332061 -74.302843
#> [33,] 97.6817381 127.155606 12.685564 253.518497 172.735024
#> [34,] 72.6193787 71.669472 64.457908 23.629672 33.708273
#> [35,] 382.0042703 234.298372 92.545413 70.597880 25.371911
#> [36,] 20.2830146 -38.976835 12.156816 101.162067 91.925428
#> [37,] -22.5861599 99.217989 174.888197 -182.603049 49.983913
#> [38,] 304.3333536 565.205832 273.229086 744.278104 128.582050
#> [39,] 405.2881770 561.858102 578.398177 46.877281 369.119806
#> [40,] 153.8193708 305.516789 671.943878 376.465117 230.222087
#> [41,] 25.3403441 -50.451534 6.821156 66.619860 -45.186210
#> [42,] 27.7561554 84.681311 198.441546 183.860494 397.731026
#> [43,] -58.6668992 79.139472 390.545862 242.839963 -195.263068
#> [44,] 36.3629705 77.191206 -19.488420 61.250836 1.878083
#> [45,] 309.9964423 -233.831332 -19.233197 33.787367 114.747715
#> [46,] 29.3782554 151.759777 45.143809 43.097343 -53.549871
#> [47,] 76.3023268 32.169418 58.076167 -6.820789 -7.758262
#> [48,] -173.2471633 413.421282 481.392544 281.629207 18.893160
#> [49,] 47.9862405 -178.137031 575.487998 140.609553 293.249665
#> [50,] 382.2241473 414.334270 67.567102 715.498675 526.397226
#> [51,] -68.7843030 113.208776 242.570581 174.905840 608.828398
#> [52,] 20.1693760 -16.571085 -15.633611 3.797942 17.079689
#> [53,] 942.3185309 689.438871 740.780746 248.080485 370.882843
#> [54,] 180.6041596 41.710512 149.711512 220.146217 214.960677
#> [55,] -60.1500863 -92.160492 99.250423 -92.589990 170.984116
#> [56,] 475.7121421 13.212757 347.285510 407.740880 208.709168
#> [57,] 942.7997674 689.920107 741.261982 248.561721 371.364080
#> [58,] 247.8414099 404.929083 440.709027 628.578663 507.167626
#> [59,] 724.4503333 76.518761 391.175806 423.285929 233.683289
#> [60,] -58.2336243 79.572747 390.979137 243.273238 -194.829793
#> [61,] -58.9418306 78.864540 390.270930 242.565032 100.812073
#> [62,] 96.0153839 86.778745 7.010134 -44.123518 80.111877
#> [63,] 12.5620024 143.840862 21.459340 71.934755 -8.804501
#> [64,] 278.7566483 156.490406 158.800986 60.978983 147.149671
#> [65,] 293.2741662 18.444312 85.617814 227.370773 375.076672
#> [66,] 36.2100001 77.038236 -19.641391 61.097865 1.725113
#> [67,] 666.9827890 371.504028 225.260998 198.911027 357.576052
#> [68,] -12.8577273 -11.920254 23.882733 27.069953 71.202862
#> [69,] 134.5470050 181.515435 288.795150 13.965296 -82.058671
#> [70,] 239.7020669 110.340261 -71.652817 605.959883 455.982087
#> [71,] 876.8966861 952.103134 370.992009 282.369821 618.746329
#> [72,] 942.5671499 689.687490 741.029365 248.329104 371.131462
#> [73,] -63.6176886 -95.628095 95.782821 -96.057592 75.621391
#> [74,] 75.2804983 76.230405 68.068934 27.240698 -28.610693
#> [75,] 452.2740498 602.251846 235.994030 106.632225 -75.360854
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#> [191,] -270.124875 387.478595 45.508681 354.36617404 433.8434459
#> [192,] 36.741906 151.211947 121.738079 58.29729173 421.3550343
#> [193,] 410.913084 -280.535610 -278.326737 464.38295123 153.9216345
#> [194,] -110.408954 56.715063 81.001962 -110.83845104 97.5432985
#> [195,] 194.090674 854.298519 18.643349 -7.21578823 398.1250907
#> [196,] 185.551397 324.127740 -50.518694 -9.94501355 131.4743850
#> [197,] 409.499141 261.793243 124.689664 120.04028387 52.8667817
#> [198,] 112.361278 45.187776 320.017630 9.00965834 165.7694847
#> [199,] 828.309997 610.211976 241.612301 351.46722617 552.2240704
#> [200,] -72.913876 -8.995123 363.197825 107.60141829 151.1100482
#>
#> $y_kernel
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> [1,] 6.169064e-03 0.017041428 0.043322644 0.05562304 0.09729685 0.10862920
#> [2,] 4.091062e-03 0.016377191 0.029407427 0.04023987 0.09856631 0.13355629
#> [3,] 7.100977e-03 0.023893003 0.040882452 0.04093324 0.04154496 0.05733597
#> [4,] 4.036171e-03 0.013102277 0.034417169 0.03946056 0.04151152 0.13729864
#> [5,] 3.406581e-02 0.036116768 0.061721311 0.07154116 0.08867961 0.10999450
#> [6,] 1.532332e-02 0.060626019 0.097184831 0.10322545 0.11274444 0.17907657
#> [7,] 3.074875e-02 0.050104130 0.061341791 0.07713280 0.07774452 0.09478476
#> [8,] 5.008228e-02 0.056669947 0.082535243 0.10818396 0.21669949 0.32545057
#> [9,] 4.060013e-02 0.045599378 0.054644728 0.06186549 0.08042905 0.09566496
#> [10,] 4.702440e-03 0.050950578 0.056136678 0.06785161 0.09446032 0.10960256
#> [11,] 3.736715e-04 0.017150204 0.019261942 0.02651127 0.07030107 0.08457038
#> [12,] 2.203195e-02 0.024325823 0.026103231 0.03357200 0.05138260 0.09582418
#> [13,] 4.567078e-02 0.083009960 0.108131159 0.11227140 0.12043543 0.12684894
#> [14,] 1.803255e-02 0.028574191 0.043824171 0.04571436 0.06303975 0.06922203
#> [15,] 3.439032e-03 0.013583274 0.016729265 0.03597171 0.04280371 0.04417686
#> [16,] 8.304338e-02 0.133243687 0.156015725 0.15987195 0.18573725 0.21662221
#> [17,] 9.333249e-05 0.062046058 0.079984841 0.09168375 0.10879468 0.11285503
#> [18,] 1.077447e-02 0.070078410 0.072085411 0.10067146 0.10734085 0.11646246
#> [19,] 6.633428e-03 0.023409960 0.025521699 0.03277103 0.06404132 0.09083014
#> [20,] 5.415611e-02 0.067038506 0.072007512 0.11767354 0.11826944 0.15654916
#> [21,] 1.510225e-02 0.019604557 0.025786833 0.04500242 0.10685913 0.11740078
#> [22,] 5.926894e-02 0.085591595 0.099724175 0.12620834 0.13323775 0.19129686
#> [23,] 1.196779e-02 0.020404819 0.037009495 0.07944094 0.08145108 0.09151553
#> [24,] 3.023275e-03 0.018212692 0.056029433 0.11782154 0.12869390 0.15497512
#> [25,] 1.106795e-02 0.099875523 0.104824198 0.10898239 0.11365037 0.14304680
#> [26,] 1.325525e-02 0.067597625 0.074566196 0.09819067 0.10982164 0.11398168
#> [27,] 1.145036e-02 0.023805076 0.085116022 0.12744377 0.12922118 0.13151505
#> [28,] 2.887157e-02 0.101580576 0.108916952 0.12027842 0.12971774 0.13836009
#> [29,] 1.543502e-03 0.044704635 0.062382620 0.07409755 0.10070626 0.10400316
#> [30,] 7.814983e-03 0.009323465 0.030638358 0.04323937 0.04529033 0.14107745
#> [31,] 1.091498e-02 0.034387720 0.070946532 0.07698715 0.08650614 0.15283827
#> [32,] 2.673617e-02 0.048769326 0.054723939 0.05670486 0.06117690 0.15826901
#> [33,] 3.828472e-03 0.015803102 0.024445450 0.03388477 0.04524624 0.04570577
#> [34,] 2.194551e-02 0.056023346 0.188684997 0.20859937 0.21270533 0.23994783
#> [35,] 2.234847e-02 0.024399423 0.059823814 0.07343866 0.07696226 0.09827715
#> [36,] 1.316851e-02 0.015366120 0.017593330 0.13988498 0.14632160 0.16636546
#> [37,] 5.494118e-03 0.011676393 0.013721465 0.01617870 0.07557818 0.08611983
#> [38,] 4.428198e-02 0.049281234 0.058326584 0.06554735 0.08411091 0.09198311
#> [39,] 3.158315e-02 0.039091589 0.055868121 0.05797986 0.06522919 0.08216432
#> [40,] 3.594768e-03 0.034962062 0.082577957 0.09272220 0.09586819 0.11511064
#> [41,] 3.550501e-02 0.039663204 0.075323642 0.08038713 0.09865579 0.16531398
#> [42,] 4.146184e-03 0.068562820 0.136650023 0.14193471 0.14225003 0.15329617
#> [43,] 3.184940e-02 0.070269719 0.166056840 0.16810780 0.19682033 0.20132264
#> [44,] 5.632561e-03 0.025546937 0.025715899 0.04265793 0.07097488 0.15820859
#> [45,] 2.670306e-02 0.043400124 0.062202768 0.07516779 0.10201374 0.10261520
#> [46,] 2.354315e-03 0.004995199 0.024586412 0.04115632 0.05566606 0.08043594
#> [47,] 2.545098e-02 0.039225827 0.063356591 0.06862226 0.07592270 0.10812585
#> [48,] 1.017029e-02 0.025740728 0.090093465 0.10415296 0.14064050 0.15498205
#> [49,] 2.604338e-02 0.038069946 0.076349671 0.07973342 0.10037727 0.13662763
#> [50,] 9.237151e-04 0.057177961 0.107675944 0.13354124 0.16569349 0.32614270
#> [51,] 3.167002e-02 0.038122983 0.044077596 0.06542208 0.06611075 0.07299715
#> [52,] 4.014587e-02 0.072349013 0.079649460 0.08895304 0.09913429 0.10537910
#> [53,] 1.397153e-02 0.015748940 0.018042816 0.07364677 0.09145736 0.10202187
#> [54,] 2.778319e-02 0.046932939 0.093058397 0.19918505 0.20019348 0.22137416
#> [55,] 1.186767e-02 0.025471508 0.050592707 0.05473294 0.10996052 0.13045964
#> [56,] 5.476710e-03 0.045070325 0.069426191 0.06982945 0.07910597 0.08453442
#> [57,] 5.874949e-03 0.007652357 0.009946232 0.06555018 0.08336078 0.11011846
#> [58,] 1.235492e-02 0.037845389 0.060617427 0.12122391 0.15953558 0.19578595
#> [59,] 1.706633e-02 0.042931626 0.149683855 0.20778553 0.22584900 0.27604931
#> [60,] 2.455975e-02 0.077559372 0.173346494 0.17539745 0.18953067 0.19403298
#> [61,] 3.647500e-02 0.065644124 0.161431245 0.16348220 0.19890659 0.20144592
#> [62,] 5.329440e-02 0.059731009 0.068997260 0.07122447 0.07977487 0.08799862
#> [63,] 1.087772e-01 0.128236931 0.135586445 0.13709413 0.15403616 0.15781854
#> [64,] 5.024230e-02 0.081727041 0.098867207 0.10940885 0.12050121 0.14168190
#> [65,] 1.827653e-02 0.039591419 0.056729867 0.09215426 0.09420522 0.12208239
#> [66,] 3.058904e-03 0.022973279 0.028289556 0.04523158 0.07354853 0.15563493
#> [67,] 8.900953e-04 0.009254147 0.012400137 0.03164259 0.03847459 0.04850599
#> [68,] 9.873471e-03 0.017173918 0.022329673 0.04657035 0.06034519 0.14915277
#> [69,] 4.672499e-02 0.067224106 0.093633928 0.11494882 0.12245169 0.12659192
#> [70,] 4.183848e-03 0.010138461 0.016591426 0.01784931 0.10129033 0.11368353
#> [71,] 1.760516e-02 0.028477527 0.044186940 0.05475874 0.09719310 0.10873295
#> [72,] 9.788632e-03 0.011566039 0.013859915 0.06946387 0.08727446 0.10620477
#> [73,] 4.647316e-02 0.083812335 0.108933533 0.11307377 0.11963306 0.12604656
#> [74,] 4.730518e-03 0.038808358 0.127931134 0.14784551 0.17919397 0.19613600
#> [75,] 3.890431e-02 0.044536717 0.066569873 0.07252449 0.07897745 0.17606955
#> [76,] 5.179553e-03 0.069292879 0.107572604 0.11095636 0.11601506 0.12098407
#> [77,] 7.665213e-02 0.089454083 0.095867588 0.10393354 0.11399131 0.11964714
#> [78,] 1.045251e-02 0.026166106 0.034232059 0.03561387 0.03739712 0.04064556
#> [79,] 6.919747e-03 0.007212833 0.033696994 0.04072641 0.09878552 0.10603485
#> [80,] 1.659297e-02 0.089301976 0.121195551 0.13255702 0.14199634 0.15063869
#> [81,] 1.344583e-02 0.021669579 0.028249287 0.02976708 0.04171344 0.04815005
#> [82,] 4.898831e-02 0.075385408 0.079791561 0.09562665 0.12590329 0.13536130
#> [83,] 1.922203e-03 0.022163447 0.024474900 0.05244009 0.06189809 0.10378092
#> [84,] 2.751422e-02 0.032483223 0.078149248 0.09368040 0.12873042 0.15779373
#> [85,] 7.726791e-02 0.093475596 0.108752654 0.11465628 0.11566471 0.12589282
#> [86,] 1.072355e-02 0.022422459 0.043593740 0.06935463 0.08853900 0.11598641
#> [87,] 1.037215e-01 0.132038419 0.133292641 0.14064216 0.14898045 0.16287425
#> [88,] 9.919854e-02 0.103512984 0.148815681 0.18263956 0.18537449 0.19141511
#> [89,] 4.675239e-03 0.014133247 0.025601400 0.04584264 0.05601607 0.07223975
#> [90,] 1.449888e-02 0.016849578 0.033791607 0.03441326 0.06210856 0.16707491
#> [91,] 2.104196e-02 0.036612400 0.093281287 0.10096514 0.14411038 0.15094238
#> [92,] 1.980711e-02 0.026941513 0.054723116 0.06229818 0.08889424 0.15939029
#> [93,] 6.906556e-03 0.011046793 0.018214643 0.05555382 0.06627437 0.08677349
#> [94,] 1.542253e-02 0.026294898 0.046369568 0.05257611 0.09937573 0.10655032
#> [95,] 2.246715e-02 0.041646180 0.060746871 0.06413062 0.08477447 0.12102484
#> [96,] 3.319924e-02 0.039635851 0.059679708 0.06790346 0.08909242 0.09131963
#> [97,] 3.474178e-02 0.055240895 0.105617139 0.11046848 0.11460871 0.12693203
#> [98,] 2.195999e-02 0.043140675 0.044149100 0.14878352 0.18026826 0.19640121
#> [99,] 1.249687e-02 0.013899658 0.020144467 0.03032571 0.07715801 0.13645653
#> [100,] 1.314760e-02 0.088971515 0.108934726 0.11098568 0.14641007 0.16354852
#> [101,] 5.003606e-03 0.026251953 0.039274767 0.07578620 0.08115759 0.08776083
#> [102,] 1.754858e-02 0.019842458 0.021619866 0.03805537 0.05586597 0.10030755
#> [103,] 6.483371e-03 0.024293968 0.049120580 0.05141446 0.05319186 0.06873555
#> [104,] 1.580481e-02 0.029497887 0.066056700 0.07209732 0.08161631 0.14794844
#> [105,] 5.717602e-03 0.063819278 0.102797928 0.17057151 0.19643680 0.26324714
#> [106,] 1.815336e-02 0.032393679 0.056749546 0.06642933 0.07185777 0.08250609
#> [107,] 3.077583e-04 0.008531510 0.028575366 0.03501198 0.04138736 0.04290515
#> [108,] 4.972594e-02 0.052393181 0.145513060 0.14756402 0.18298841 0.20012686
#> [109,] 7.003153e-03 0.024439071 0.029230925 0.03483094 0.10291814 0.15128366
#> [110,] 9.483870e-03 0.028827796 0.065078165 0.07009035 0.08572201 0.08910576
#> [111,] 3.354040e-03 0.025387196 0.031341809 0.03779477 0.08008699 0.13488688
#> [112,] 7.969270e-03 0.015544338 0.050460346 0.08912283 0.09557580 0.09720897
#> [113,] 1.436518e-02 0.087753939 0.179336107 0.18354106 0.18383842 0.18559202
#> [114,] 2.408689e-03 0.004520427 0.004840639 0.02129696 0.06289975 0.06992917
#> [115,] 7.907821e-03 0.029143787 0.045098338 0.10689044 0.11776280 0.14404402
#> [116,] 2.186734e-02 0.039924765 0.050797129 0.07487350 0.07707834 0.09610946
#> [117,] 6.780352e-03 0.010359814 0.017321997 0.04184455 0.07917871 0.09839430
#> [118,] 7.805943e-02 0.088046780 0.094460285 0.10252624 0.11539861 0.11823984
#> [119,] 3.422719e-03 0.012880726 0.026853920 0.04709516 0.05476355 0.07349227
#> [120,] 3.273590e-02 0.039149408 0.047215361 0.06292896 0.10899534 0.11077859
#> [121,] 4.607565e-02 0.057437117 0.066876441 0.07551879 0.08749342 0.09171287
#> [122,] 2.389726e-02 0.050294367 0.070535612 0.10081225 0.10488260 0.11027026
#> [123,] 1.081911e-03 0.071627093 0.138870435 0.13971430 0.14531431 0.15023190
#> [124,] 1.528702e-03 0.043773995 0.080332807 0.08637343 0.09589242 0.16222455
#> [125,] 5.161903e-03 0.011344179 0.014053679 0.01584649 0.07591040 0.08645204
#> [126,] 2.765505e-02 0.129774174 0.137315873 0.14181818 0.14800046 0.16721604
#> [127,] 8.447186e-03 0.067745708 0.081207696 0.08261048 0.08885529 0.09903653
#> [128,] 4.508682e-02 0.066267507 0.067275931 0.12565669 0.15714143 0.17428160
#> [129,] 9.415642e-02 0.122473364 0.139415393 0.14285770 0.15020721 0.17076385
#> [130,] 6.422508e-04 0.135622837 0.140622089 0.14550278 0.14966744 0.15688820
#> [131,] 4.009404e-02 0.042145001 0.055693078 0.07756939 0.09470784 0.11602273
#> [132,] 6.715408e-02 0.112456778 0.135557438 0.14901559 0.15505621 0.16457520
#> [133,] 2.751988e-05 0.003173510 0.010116722 0.02241596 0.02924796 0.05773262
#> [134,] 3.417119e-02 0.068249031 0.098490461 0.11840484 0.14975330 0.16669533
#> [135,] 4.275856e-03 0.017039037 0.034177485 0.06960188 0.07165283 0.14463478
#> [136,] 3.896528e-02 0.041192490 0.069727123 0.08332637 0.08976299 0.10980685
#> [137,] 1.622036e-02 0.088929363 0.121568165 0.13292963 0.14236896 0.15101130
#> [138,] 4.718553e-02 0.097385840 0.120157878 0.18076436 0.19572980 0.21907603
#> [139,] 7.480029e-03 0.008882812 0.015127621 0.02530887 0.08217485 0.14147337
#> [140,] 5.836622e-02 0.065715739 0.087947836 0.10451774 0.11902748 0.14379736
#> [141,] 1.496433e-02 0.017015284 0.020460064 0.03759851 0.05891341 0.11280241
#> [142,] 2.188905e-02 0.027088234 0.035525265 0.06633063 0.08414123 0.09456139
#> [143,] 3.633786e-04 0.021599345 0.052642780 0.11443488 0.12530725 0.15158846
#> [144,] 3.818535e-03 0.005802092 0.072134225 0.08165321 0.08769383 0.12425265
#> [145,] 5.305818e-02 0.055457351 0.111159855 0.21590656 0.21791208 0.24377738
#> [146,] 7.742970e-02 0.088676516 0.095090022 0.10315598 0.11476887 0.11886958
#> [147,] 2.351494e-02 0.027032099 0.047870803 0.05755058 0.06297903 0.09138484
#> [148,] 3.220160e-02 0.076313930 0.134415607 0.19265081 0.23120764 0.24116784
#> [149,] 7.646770e-03 0.025082688 0.061316767 0.06691678 0.11919782 0.12881845
#> [150,] 3.954823e-02 0.073626074 0.093113418 0.11302779 0.14437625 0.16131828
#> [151,] 6.679428e-03 0.023376495 0.042179139 0.05514416 0.08259158 0.12203737
#> [152,] 6.150445e-02 0.066503702 0.074760638 0.07554905 0.08276981 0.10133338
#> [153,] 7.525553e-03 0.031031277 0.055141448 0.06528569 0.06843168 0.08767413
#> [154,] 9.239889e-02 0.099748405 0.121980502 0.13855041 0.14461522 0.15306015
#> [155,] 1.604288e-02 0.033491369 0.045465999 0.04729844 0.05410835 0.06354767
#> [156,] 2.251231e-02 0.038094170 0.060823980 0.06086621 0.09707435 0.11106652
#> [157,] 2.672884e-02 0.065285667 0.112901562 0.12304580 0.12619179 0.13372038
#> [158,] 1.134723e-01 0.120821830 0.123541797 0.14305393 0.15185875 0.15962383
#> [159,] 1.249720e-02 0.012819170 0.023651614 0.03296545 0.08197806 0.11696803
#> [160,] 4.676452e-04 0.014042098 0.025237521 0.02702077 0.03061200 0.05284410
#> [161,] 2.313159e-02 0.051666219 0.053893429 0.17618508 0.18262170 0.20266555
#> [162,] 5.363280e-02 0.084155729 0.095517195 0.10495652 0.11359887 0.12557350
#> [163,] 7.910492e-03 0.056442244 0.058457528 0.07201268 0.08281339 0.09249317
#> [164,] 8.625900e-04 0.005319686 0.005364900 0.02453527 0.08639198 0.09693363
#> [165,] 2.052586e-02 0.043826872 0.059397309 0.07107290 0.09542877 0.10510855
#> [166,] 2.352272e-02 0.034355164 0.034803722 0.05967153 0.06979370 0.08013978
#> [167,] 1.809056e-02 0.090424969 0.148526645 0.17853977 0.21709660 0.25527887
#> [168,] 1.243599e-02 0.033616675 0.034625099 0.15830752 0.18687721 0.18979226
#> [169,] 8.403267e-03 0.012543503 0.037664702 0.04682431 0.06732343 0.07500388
#> [170,] 1.034431e-02 0.048901142 0.096517037 0.10666128 0.10980727 0.12904972
#> [171,] 2.066036e-02 0.036230797 0.093662890 0.10058353 0.14449198 0.15113057
#> [172,] 1.520158e-02 0.021048788 0.035845423 0.03922918 0.05936045 0.07750890
#> [173,] 2.977375e-02 0.051088645 0.068227093 0.10365148 0.10570244 0.11058517
#> [174,] 7.743501e-02 0.105969640 0.108196850 0.15721583 0.19129367 0.23048850
#> [175,] 7.915666e-03 0.020401282 0.024857695 0.05620616 0.07612053 0.20878218
#> [176,] 3.327572e-02 0.104512800 0.105984727 0.11587427 0.12531359 0.13395594
#> [177,] 1.544643e-02 0.029498832 0.036617710 0.04831662 0.05694624 0.06991127
#> [178,] 1.240528e-02 0.017404532 0.026449881 0.03367064 0.05223421 0.10021764
#> [179,] 5.035352e-02 0.054511714 0.065538625 0.09017215 0.11350430 0.15434620
#> [180,] 7.182935e-04 0.021217407 0.054509287 0.05864952 0.08377072 0.12110990
#> [181,] 2.503666e-02 0.039076663 0.063316387 0.06670014 0.08734398 0.12359435
#> [182,] 7.203424e-03 0.039545197 0.069156149 0.07446120 0.08203627 0.14923432
#> [183,] 8.012054e-02 0.108655172 0.110882382 0.15453030 0.18860814 0.23317404
#> [184,] 4.481558e-02 0.060386020 0.069507668 0.12033676 0.12473876 0.12716876
#> [185,] 7.487187e-03 0.028802080 0.045940528 0.08136492 0.08341588 0.13287173
#> [186,] 1.591690e-03 0.008088090 0.013516536 0.02594756 0.04677450 0.07649459
#> [187,] 7.038888e-03 0.014613955 0.049529963 0.09005321 0.09627858 0.09650618
#> [188,] 1.155886e-02 0.069660541 0.095193364 0.12105866 0.17817607 0.33862528
#> [189,] 3.931122e-02 0.056008286 0.074810929 0.08777595 0.08940558 0.11522337
#> [190,] 1.039584e-03 0.002048009 0.023228697 0.15121253 0.19397221 0.22545695
#> [191,] 9.127505e-02 0.111436472 0.156739169 0.17471607 0.19329798 0.19674923
#> [192,] 2.163598e-02 0.039071896 0.075305975 0.08090599 0.10520862 0.11482924
#> [193,] 3.598530e-02 0.071240739 0.080008105 0.08178551 0.08407939 0.13255168
#> [194,] 4.844063e-03 0.011725842 0.026235585 0.02707616 0.03442567 0.05100546
#> [195,] 3.888340e-03 0.014675225 0.021895987 0.03094134 0.03594059 0.05187177
#> [196,] 1.081054e-03 0.010617858 0.022252335 0.06719760 0.09069603 0.09464501
#> [197,] 2.621252e-03 0.019761418 0.028863488 0.03030306 0.09215978 0.11137536
#> [198,] 7.135820e-03 0.011638130 0.017820406 0.03703599 0.09889270 0.10943435
#> [199,] 8.235232e-03 0.020309819 0.050800892 0.05923792 0.07428402 0.10056524
#> [200,] 3.962802e-02 0.060808708 0.061817133 0.13111549 0.16260023 0.17974040
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> [1,] 0.10937143 0.12986516 0.16840756 0.17684459 0.22582187 0.2702635
#> [2,] 0.14395004 0.19075324 0.20589548 0.23250419 0.24421912 0.3050582
#> [3,] 0.05944602 0.06666678 0.07571213 0.08071138 0.08792901 0.1687819
#> [4,] 0.17477609 0.19527520 0.23941776 0.25050278 0.25464302 0.2797642
#> [5,] 0.16384043 0.25035342 0.27085253 0.32608011 0.32881136 0.3302204
#> [6,] 0.18738820 0.18869720 0.27082922 0.29286238 0.29881699 0.3052700
#> [7,] 0.11141508 0.11157678 0.14667051 0.15956021 0.17812377 0.1853445
#> [8,] 0.37565088 0.37714870 0.39842292 0.41570553 0.45902940 0.4633214
#> [9,] 0.12841248 0.14520451 0.16224474 0.16285646 0.17864747 0.2092405
#> [10,] 0.11024910 0.15640575 0.16679951 0.19990398 0.20130676 0.2017895
#> [11,] 0.09159980 0.11808396 0.12088224 0.13221654 0.16654826 0.1715173
#> [12,] 0.14209664 0.14480147 0.15323850 0.17735208 0.21227462 0.2243492
#> [13,] 0.13491489 0.15062849 0.16749898 0.18799809 0.19669487 0.1984781
#> [14,] 0.07372434 0.07719910 0.23869527 0.24794261 0.26912330 0.2701317
#> [15,] 0.08273369 0.09363281 0.20795606 0.22352649 0.24318291 0.2878792
#> [16,] 0.25493388 0.29118424 0.29248948 0.31182809 0.31521184 0.3505912
#> [17,] 0.14371069 0.15128575 0.15780029 0.18524771 0.19821273 0.2170154
#> [18,] 0.11707418 0.13411442 0.15090645 0.19888987 0.21745344 0.2233343
#> [19,] 0.09785955 0.11462248 0.12434371 0.13847629 0.16028851 0.1652575
#> [20,] 0.15993292 0.16825470 0.18057676 0.21682713 0.23892945 0.2551388
#> [21,] 0.13454094 0.14986868 0.16602568 0.25198780 0.33676919 0.3477749
#> [22,] 0.19553403 0.19854619 0.20053328 0.20065793 0.20957863 0.2167994
#> [23,] 0.09926167 0.14548973 0.15486563 0.15715950 0.15893691 0.1717709
#> [24,] 0.20894932 0.22102391 0.28006003 0.28849706 0.33747434 0.3819159
#> [25,] 0.14464283 0.15034724 0.16797498 0.18255039 0.23463316 0.2361510
#> [26,] 0.11459340 0.13163363 0.14842566 0.19640909 0.21497265 0.2221934
#> [27,] 0.16596890 0.18711900 0.19656194 0.20492960 0.21235295 0.2129647
#> [28,] 0.15033472 0.16966778 0.17526779 0.19986897 0.21150187 0.2289378
#> [29,] 0.11584850 0.16265170 0.17304545 0.19365804 0.19506082 0.2013056
#> [30,] 0.17099728 0.19149639 0.24319657 0.24672397 0.25086421 0.2759854
#> [31,] 0.16245890 0.21362650 0.28930349 0.29706752 0.30673941 0.3191007
#> [32,] 0.16584407 0.20076008 0.24750870 0.25941637 0.30471907 0.3094614
#> [33,] 0.07696133 0.11123249 0.15311532 0.16257332 0.18303476 0.1928500
#> [34,] 0.24123997 0.24346718 0.25688986 0.28520681 0.36575883 0.3721954
#> [35,] 0.17555778 0.23863608 0.25913519 0.31436277 0.31850301 0.3405287
#> [36,] 0.17458921 0.21628432 0.21780211 0.24781935 0.28189719 0.2844603
#> [37,] 0.10325999 0.13474473 0.18114963 0.28326875 0.30548824 0.3266689
#> [38,] 0.13209434 0.14888637 0.16592660 0.16653832 0.18232933 0.2129224
#> [39,] 0.12328830 0.12783035 0.13031771 0.13279935 0.15680188 0.1709345
#> [40,] 0.12194264 0.16404398 0.17277173 0.27255951 0.28709498 0.3026654
#> [41,] 0.16683177 0.16919471 0.18296955 0.20852688 0.21236598 0.2167506
#> [42,] 0.16273550 0.17137785 0.17848411 0.18335248 0.19592003 0.2328867
#> [43,] 0.20353219 0.20750491 0.22067064 0.22672050 0.24198553 0.2885772
#> [44,] 0.19228643 0.30798899 0.31533850 0.33757060 0.35414051 0.3686502
#> [45,] 0.13527170 0.14070015 0.14756047 0.15037993 0.16873175 0.1747358
#> [46,] 0.08221919 0.12828556 0.14399916 0.15206512 0.15847862 0.2420093
#> [47,] 0.17924874 0.18340693 0.21906737 0.23722476 0.24239952 0.2474060
#> [48,] 0.16181405 0.16499637 0.17467615 0.18010459 0.18105650 0.1842025
#> [49,] 0.14723800 0.15220700 0.17493930 0.19787303 0.23554578 0.2484542
#> [50,] 0.36469953 0.37645657 0.41231543 0.42245967 0.42560566 0.4266569
#> [51,] 0.10791316 0.14955178 0.15466178 0.21661451 0.29669268 0.3083916
#> [52,] 0.10678188 0.10904589 0.12282073 0.19643676 0.21162831 0.2557353
#> [53,] 0.13589895 0.13727731 0.18487623 0.19331326 0.19858826 0.2523494
#> [54,] 0.22183826 0.24823537 0.26847661 0.29875325 0.30821126 0.3500941
#> [55,] 0.17797388 0.18438739 0.19245334 0.20816694 0.25423332 0.2560166
#> [56,] 0.08539988 0.11779238 0.19972313 0.24650918 0.25055223 0.2573842
#> [57,] 0.12780236 0.14537390 0.17677965 0.18521668 0.20668484 0.2442528
#> [58,] 0.21642979 0.21981354 0.25527025 0.25809327 0.28113555 0.3222066
#> [59,] 0.29882135 0.31630106 0.35942783 0.39773950 0.43398987 0.4546337
#> [60,] 0.20021526 0.21082184 0.21943084 0.22796029 0.24927518 0.2812876
#> [61,] 0.20594823 0.21213051 0.21604504 0.23134609 0.23735993 0.2932028
#> [62,] 0.09975910 0.12969373 0.13121152 0.19786971 0.22120186 0.2568623
#> [63,] 0.17438845 0.18538462 0.18889819 0.20529899 0.21366807 0.2154513
#> [64,] 0.14269032 0.17126557 0.19048115 0.19666343 0.20116574 0.2949424
#> [65,] 0.14258151 0.18999234 0.19780909 0.20194933 0.22707052 0.2644097
#> [66,] 0.18971277 0.31056264 0.31791216 0.34014426 0.35671416 0.3712239
#> [67,] 0.08706282 0.08930368 0.20362693 0.21919737 0.24751203 0.2835501
#> [68,] 0.15142858 0.16160983 0.16785464 0.16925742 0.25891230 0.2650449
#> [69,] 0.13208727 0.15171312 0.16751166 0.16956262 0.18905230 0.2653497
#> [70,] 0.12125860 0.15617460 0.20292323 0.26487595 0.30400185 0.3449541
#> [71,] 0.11842906 0.12080753 0.17984366 0.18828069 0.23725797 0.2816996
#> [72,] 0.13171604 0.14146021 0.18069333 0.18913036 0.20277116 0.2481665
#> [73,] 0.13411251 0.14982611 0.16830135 0.18880046 0.19589249 0.1976757
#> [74,] 0.22445295 0.27345920 0.30199383 0.30422104 0.42651269 0.4329493
#> [75,] 0.18364462 0.21856063 0.24161583 0.26530925 0.28691852 0.3234773
#> [76,] 0.13160020 0.16665009 0.16785057 0.20616223 0.21723126 0.2667687
#> [77,] 0.13911251 0.14325274 0.16571352 0.16749677 0.19226664 0.1984803
#> [78,] 0.06216700 0.07667674 0.09324664 0.11547874 0.12282826 0.2067518
#> [79,] 0.10814659 0.12492312 0.15178028 0.19559786 0.24617903 0.2880454
#> [80,] 0.15738918 0.16261332 0.16298919 0.19922327 0.21214757 0.2166592
#> [81,] 0.09642526 0.11975741 0.15541785 0.15957604 0.17044171 0.1726689
#> [82,] 0.14506677 0.17724412 0.21151528 0.21978290 0.24277084 0.2923051
#> [83,] 0.13805208 0.15325477 0.16930764 0.21852997 0.21884188 0.2308165
#> [84,] 0.19607345 0.19940516 0.19945720 0.21618169 0.21829343 0.2201010
#> [85,] 0.13643447 0.19829118 0.21750676 0.22368904 0.22819135 0.2679168
#> [86,] 0.12895144 0.13130735 0.14775408 0.16445115 0.17805597 0.2129720
#> [87,] 0.17944416 0.18032891 0.19395390 0.20024328 0.21872378 0.2205070
#> [88,] 0.20093410 0.20467272 0.21062733 0.21708030 0.26726623 0.2768869
#> [89,] 0.09028723 0.12154279 0.17107703 0.18305166 0.19169401 0.2010196
#> [90,] 0.20115275 0.29912267 0.30647218 0.32870428 0.34527418 0.3597839
#> [91,] 0.15151217 0.17018483 0.17333082 0.17586804 0.18347506 0.1855478
#> [92,] 0.16584325 0.16897241 0.17179786 0.18067132 0.19383102 0.2018426
#> [93,] 0.22166003 0.22713241 0.22807354 0.23613949 0.24844730 0.2518531
#> [94,] 0.11862490 0.12061169 0.17766103 0.18609806 0.23507534 0.2795169
#> [95,] 0.15933650 0.16284080 0.16780980 0.21347583 0.21994299 0.2427150
#> [96,] 0.10959857 0.11111637 0.11985426 0.17777455 0.20110670 0.2367671
#> [97,] 0.13972991 0.14407048 0.17706909 0.17949487 0.18154583 0.2773330
#> [98,] 0.19740843 0.20795007 0.26980679 0.27111734 0.28902237 0.2952046
#> [99,] 0.15942462 0.18270467 0.19162777 0.19892822 0.22832464 0.2420995
#> [100,] 0.18486342 0.25394244 0.25844475 0.26462703 0.28384261 0.3252223
#> [101,] 0.09061560 0.09640318 0.10584250 0.11720397 0.12089224 0.1411335
#> [102,] 0.13761327 0.14928483 0.15772186 0.17286871 0.21675799 0.2288326
#> [103,] 0.11771283 0.12614986 0.16918527 0.18518599 0.19726057 0.2044407
#> [104,] 0.15756907 0.21851633 0.28441366 0.30184958 0.30195735 0.3239905
#> [105,] 0.30180397 0.34941987 0.35956411 0.36271010 0.38195255 0.3887845
#> [106,] 0.09807653 0.10511573 0.21239978 0.23383253 0.25052960 0.2632289
#> [107,] 0.10956333 0.13289548 0.15730364 0.15953085 0.16855592 0.1727141
#> [108,] 0.21736411 0.22144175 0.22186642 0.22804869 0.24726428 0.3091210
#> [109,] 0.16090429 0.17562714 0.22723643 0.23675542 0.24279603 0.2793548
#> [110,] 0.09286239 0.12738548 0.14306270 0.19149881 0.31269343 0.3176624
#> [111,] 0.14246194 0.17737795 0.22412657 0.28279850 0.28607930 0.3281012
#> [112,] 0.10153041 0.12356357 0.15916169 0.20700459 0.23923987 0.2509388
#> [113,] 0.19002069 0.20923628 0.22101641 0.23815486 0.25946975 0.2710930
#> [114,] 0.09197170 0.09641333 0.11054591 0.14255287 0.18821889 0.1931879
#> [115,] 0.19801822 0.21009281 0.26912893 0.27756596 0.32654325 0.3709848
#> [116,] 0.13105255 0.14312713 0.20216326 0.21060029 0.25957757 0.3040192
#> [117,] 0.10457657 0.10907888 0.21258806 0.23376875 0.23477718 0.2740498
#> [118,] 0.14051981 0.14466005 0.16430622 0.16608946 0.19085934 0.1998876
#> [119,] 0.08903471 0.12029027 0.16982451 0.18179914 0.19044149 0.1998808
#> [120,] 0.13337031 0.13554846 0.15005821 0.16662811 0.17070949 0.1888602
#> [121,] 0.13702767 0.16442188 0.16828322 0.20255439 0.23250908 0.2381091
#> [122,] 0.15215308 0.17015781 0.18642424 0.21767980 0.24487394 0.2672140
#> [123,] 0.15967123 0.16831357 0.18028820 0.18154838 0.19898430 0.2298224
#> [124,] 0.17184518 0.20424022 0.28768125 0.29868977 0.30971440 0.3156690
#> [125,] 0.10359221 0.13507695 0.18081742 0.28293654 0.30582046 0.3270011
#> [126,] 0.22556130 0.22761225 0.22907276 0.23961440 0.25675457 0.2630366
#> [127,] 0.11399385 0.17483296 0.18654789 0.21315660 0.22813544 0.2282988
#> [128,] 0.18482324 0.21952804 0.24667996 0.26589554 0.27207782 0.2765801
#> [129,] 0.17243931 0.18900921 0.19067823 0.20351896 0.22828883 0.2300721
#> [130,] 0.15963536 0.17545177 0.18611952 0.19314894 0.22343519 0.2402272
#> [131,] 0.15781220 0.25638165 0.27688077 0.32278312 0.32728543 0.3321083
#> [132,] 0.21899846 0.23090733 0.24052796 0.24103162 0.24698623 0.2534392
#> [133,] 0.08007705 0.09628945 0.19440030 0.20997074 0.25673866 0.2743235
#> [134,] 0.19501227 0.30289987 0.33143450 0.33366171 0.43202639 0.4393759
#> [135,] 0.16513389 0.16743996 0.22036147 0.22450171 0.24962291 0.2695591
#> [136,] 0.11803060 0.15972571 0.16124350 0.22790169 0.25123384 0.2868943
#> [137,] 0.15701657 0.16261658 0.16298593 0.19885066 0.21252018 0.2162866
#> [138,] 0.22159509 0.25532640 0.27597024 0.27935399 0.31763372 0.3283473
#> [139,] 0.15440778 0.18661092 0.18772151 0.19391137 0.22330780 0.2370826
#> [140,] 0.14558061 0.17864789 0.19164699 0.20696484 0.20736059 0.2154265
#> [141,] 0.19927233 0.21492153 0.21977144 0.27499902 0.27913926 0.3042605
#> [142,] 0.10663598 0.13974518 0.14203905 0.14381646 0.16061018 0.1868914
#> [143,] 0.20556267 0.21763725 0.27667338 0.28511041 0.33408769 0.3785293
#> [144,] 0.13066313 0.14809905 0.16955534 0.18433313 0.18993314 0.2580203
#> [145,] 0.25446339 0.30207929 0.31222353 0.31536952 0.33461197 0.3414440
#> [146,] 0.13989007 0.14403031 0.16493595 0.16671920 0.19148908 0.1992579
#> [147,] 0.09623699 0.10695527 0.22127852 0.22495379 0.24165086 0.2604535
#> [148,] 0.26703313 0.27882354 0.28896778 0.29211377 0.31135622 0.3181882
#> [149,] 0.13500398 0.19515058 0.20466957 0.20771298 0.21071019 0.2472690
#> [150,] 0.18963523 0.30827691 0.33681154 0.33903875 0.42664934 0.4339989
#> [151,] 0.12753684 0.14870812 0.15529533 0.16040703 0.16072378 0.1704036
#> [152,] 0.14931681 0.16610883 0.18314907 0.18376079 0.19955180 0.2196212
#> [153,] 0.09450613 0.14533522 0.19148049 0.25965847 0.27522891 0.2999960
#> [154,] 0.17293217 0.17783003 0.17961328 0.18987420 0.22122266 0.2256797
#> [155,] 0.07490914 0.08156960 0.12345242 0.13291043 0.16318707 0.1834283
#> [156,] 0.11771819 0.12110194 0.15938167 0.22349499 0.34468961 0.3496586
#> [157,] 0.14543424 0.15226624 0.20309534 0.24223591 0.30033758 0.3174186
#> [158,] 0.16880077 0.17413358 0.19890345 0.20014923 0.20068670 0.2200636
#> [159,] 0.12736178 0.17416498 0.18930722 0.21591593 0.22763086 0.2884700
#> [160,] 0.06019362 0.07308715 0.08880075 0.09686670 0.10328021 0.2693864
#> [161,] 0.21088931 0.21151925 0.24559709 0.25258442 0.25410221 0.3207604
#> [162,] 0.12634180 0.17510774 0.19442900 0.20002901 0.20636330 0.2362631
#> [163,] 0.09792162 0.13117958 0.18633593 0.23716502 0.24399703 0.2598964
#> [164,] 0.11407380 0.14555854 0.17033583 0.27245495 0.31630205 0.3374827
#> [165,] 0.11053699 0.14379495 0.17372056 0.22454965 0.23138165 0.2506241
#> [166,] 0.08018745 0.12699065 0.14213289 0.16874160 0.18045652 0.2412956
#> [167,] 0.26471250 0.27485674 0.27800273 0.28114417 0.29724518 0.3040772
#> [168,] 0.20693243 0.21747407 0.26159334 0.27933079 0.29854637 0.3047286
#> [169,] 0.20768235 0.22899724 0.24111009 0.24613569 0.24752360 0.2555896
#> [170,] 0.13588172 0.15010490 0.18671081 0.25862043 0.30103406 0.3166045
#> [171,] 0.15132398 0.17056643 0.17371242 0.17548644 0.18385666 0.1851662
#> [172,] 0.11996694 0.14162223 0.14273898 0.19293928 0.26281684 0.2677858
#> [173,] 0.13108428 0.18631186 0.19045210 0.20148956 0.21557330 0.2529125
#> [174,] 0.23692512 0.25696898 0.26519273 0.30688784 0.30840563 0.3239553
#> [175,] 0.24286002 0.25741539 0.26476491 0.28699701 0.30356691 0.3180767
#> [176,] 0.14593057 0.17407193 0.17967194 0.19546481 0.21590602 0.2267204
#> [177,] 0.08871391 0.10541098 0.12839480 0.19034752 0.23412778 0.2370961
#> [178,] 0.11700966 0.12385981 0.13404990 0.13466162 0.15045263 0.1810457
#> [179,] 0.16812104 0.18016249 0.18168028 0.19751747 0.20481792 0.2233754
#> [180,] 0.16157633 0.18289122 0.20002967 0.23545406 0.23750502 0.2872161
#> [181,] 0.16027128 0.16190602 0.16524029 0.21090631 0.22251250 0.2452845
#> [182,] 0.16093323 0.17912837 0.18210452 0.18558134 0.19153595 0.2135691
#> [183,] 0.23961065 0.25965451 0.26787826 0.30957337 0.31109117 0.3212698
#> [184,] 0.14641121 0.14955720 0.15970144 0.17528579 0.19964166 0.2073173
#> [185,] 0.15337085 0.17920300 0.20859843 0.21273866 0.23785986 0.2751990
#> [186,] 0.14084733 0.15641776 0.17549130 0.19218836 0.21099101 0.2239560
#> [187,] 0.10246079 0.12449395 0.15823131 0.20793497 0.23830948 0.2500084
#> [188,] 0.36397399 0.37718211 0.41417430 0.42479801 0.43494225 0.4369463
#> [189,] 0.12266354 0.12809199 0.13777177 0.16016863 0.16212763 0.1813399
#> [190,] 0.22592866 0.24259711 0.25313876 0.29120386 0.31499548 0.3342111
#> [191,] 0.19933860 0.20270384 0.20885759 0.20915681 0.27518972 0.2848103
#> [192,] 0.14899319 0.18116138 0.19068037 0.19672098 0.22170219 0.2332798
#> [193,] 0.13968334 0.15749394 0.20193552 0.21340456 0.24399761 0.2509128
#> [194,] 0.05278871 0.09885509 0.11456869 0.12263464 0.12904815 0.2714398
#> [195,] 0.06866379 0.08570403 0.08631575 0.10210676 0.13269980 0.1722057
#> [196,] 0.10761003 0.12641268 0.14310974 0.15264876 0.19939738 0.2343134
#> [197,] 0.11755764 0.12205995 0.19960700 0.22078769 0.22179611 0.2870309
#> [198,] 0.12657452 0.15783511 0.15805926 0.25995423 0.32880277 0.3499835
#> [199,] 0.10821521 0.11143760 0.15265679 0.17046739 0.17322970 0.2260713
#> [200,] 0.19028204 0.21406925 0.25213876 0.27135434 0.27753662 0.2820389
#> [,13] [,14] [,15] [,16] [,17] [,18] [,19]
#> [1,] 0.2880741 0.3436780 0.3459719 0.3477493 0.4637427 0.4989981 0.5603091
#> [2,] 0.3513064 0.4106049 0.5002598 0.5016626 0.5079074 0.5180886 0.6471875
#> [3,] 0.2169765 0.2300928 0.2653483 0.3618370 0.3759696 0.3813417 0.3831191
#> [4,] 0.3171034 0.4043887 0.4088910 0.4150733 0.4342889 0.4832096 0.4896231
#> [5,] 0.3333137 0.3394959 0.3553416 0.3587115 0.3926807 0.4205682 0.4311099
#> [6,] 0.3155418 0.3329777 0.3692118 0.3748118 0.4023621 0.4099371 0.4428990
#> [7,] 0.1943899 0.1993891 0.2626639 0.2644413 0.2667352 0.3223392 0.3356542
#> [8,] 0.4734657 0.4766117 0.4958541 0.4973411 0.5026861 0.5335914 0.5535152
#> [9,] 0.2405255 0.2546581 0.2811422 0.2881717 0.2900934 0.3462308 0.3514043
#> [10,] 0.2075516 0.2177328 0.2601159 0.2709484 0.2962647 0.3167330 0.3468317
#> [11,] 0.2770771 0.2927119 0.3568252 0.3951049 0.3984887 0.4133422 0.4183414
#> [12,] 0.2386630 0.2783234 0.3046046 0.3154770 0.3195159 0.3501089 0.3659000
#> [13,] 0.2232480 0.2377577 0.2543276 0.2765597 0.2839093 0.3283570 0.3496719
#> [14,] 0.3408144 0.4223838 0.4366015 0.4386525 0.4740769 0.4912153 0.4971000
#> [15,] 0.3384263 0.3516984 0.3627821 0.3724619 0.3778904 0.4098001 0.4111483
#> [16,] 0.3534916 0.4176049 0.4591067 0.5387995 0.5437685 0.5894345 0.6195559
#> [17,] 0.2337124 0.2483779 0.2548308 0.2607854 0.2828186 0.3624292 0.3662596
#> [18,] 0.2246742 0.2251117 0.2274055 0.2337196 0.2387188 0.2830095 0.3008201
#> [19,] 0.2833368 0.2864521 0.3505655 0.3888452 0.3922289 0.4128728 0.4196019
#> [20,] 0.2557060 0.2578177 0.2650670 0.3157453 0.3231262 0.3301556 0.3385173
#> [21,] 0.3498259 0.3579499 0.3589583 0.3852503 0.4023887 0.4237036 0.5112104
#> [22,] 0.2174345 0.2353630 0.2833464 0.2881092 0.3001384 0.3171786 0.3177904
#> [23,] 0.1826433 0.2444354 0.2749303 0.2974416 0.3101858 0.3186775 0.3714967
#> [24,] 0.3997265 0.4553305 0.4576243 0.4594018 0.5753952 0.6106506 0.6719615
#> [25,] 0.2778461 0.2860698 0.3061137 0.3116493 0.3125503 0.3218305 0.3280754
#> [26,] 0.2258150 0.2275924 0.2298863 0.2312388 0.2362380 0.2854903 0.3033009
#> [27,] 0.2300049 0.2467969 0.2493712 0.2947804 0.2983485 0.3067855 0.3133439
#> [28,] 0.2311245 0.2653957 0.3072785 0.3167365 0.3470132 0.3557824 0.3654030
#> [29,] 0.2080354 0.2114869 0.2663619 0.2771943 0.3025107 0.3229789 0.3405858
#> [30,] 0.3133246 0.4081675 0.4126698 0.4188521 0.4380677 0.4794308 0.4858443
#> [31,] 0.3250553 0.3315083 0.3429735 0.3485735 0.4166607 0.4286004 0.4361754
#> [32,] 0.3412779 0.3473185 0.3568375 0.3895396 0.4012385 0.4224098 0.4231696
#> [33,] 0.2130912 0.2394883 0.2557438 0.3238310 0.3294310 0.3656651 0.3682682
#> [34,] 0.3922393 0.4004631 0.4421582 0.4436760 0.5103341 0.5222209 0.5295704
#> [35,] 0.3436242 0.3450310 0.3512133 0.3704289 0.3809634 0.4322856 0.4428272
#> [36,] 0.3077924 0.3434529 0.3476111 0.4145588 0.4344732 0.4635032 0.4658217
#> [37,] 0.3276774 0.3790559 0.3811068 0.4165312 0.4336697 0.4549846 0.4799295
#> [38,] 0.2368436 0.2509762 0.2774604 0.2844898 0.2937752 0.3425489 0.3497982
#> [39,] 0.2539940 0.3157950 0.3181073 0.3563870 0.3597708 0.3804146 0.4166650
#> [40,] 0.3306612 0.3670182 0.4175652 0.4374134 0.4419211 0.4516008 0.4570293
#> [41,] 0.2196664 0.2367945 0.2432311 0.2518696 0.3655228 0.3677500 0.3809685
#> [42,] 0.2641423 0.2984134 0.3227646 0.3323853 0.3402963 0.3497543 0.3800309
#> [43,] 0.2991189 0.3162590 0.3477438 0.3823445 0.4028436 0.4580711 0.4622114
#> [44,] 0.3934201 0.3952034 0.4269373 0.4412697 0.4554719 0.4569833 0.4576991
#> [45,] 0.1804307 0.2252828 0.2605088 0.2896356 0.3052060 0.3224616 0.3692102
#> [46,] 0.2703263 0.2872683 0.3186167 0.3245848 0.3385311 0.3619240 0.3870452
#> [47,] 0.2536508 0.2550536 0.3090577 0.3105755 0.3447085 0.3522706 0.3604944
#> [48,] 0.1943467 0.2133626 0.2419626 0.2805195 0.3420794 0.3587764 0.3775791
#> [49,] 0.2583178 0.3085181 0.3191289 0.3359055 0.3380172 0.3452665 0.4033256
#> [50,] 0.4448481 0.4494289 0.4516801 0.5025092 0.5100354 0.5483471 0.5845974
#> [51,] 0.3295629 0.3522633 0.3745081 0.3975660 0.4019555 0.4149206 0.4337232
#> [52,] 0.3019834 0.3275205 0.3316786 0.3628225 0.3673391 0.3745375 0.3906712
#> [53,] 0.2644240 0.2794411 0.3100342 0.3183982 0.3258252 0.3264369 0.3434771
#> [54,] 0.3843652 0.3921177 0.4156208 0.4236024 0.4407426 0.4512842 0.4651550
#> [55,] 0.2708186 0.2807864 0.2921335 0.2952962 0.3092719 0.3118661 0.3340982
#> [56,] 0.2632062 0.2766267 0.2797727 0.2820089 0.2899169 0.2949739 0.3224213
#> [57,] 0.2563274 0.2875377 0.3103016 0.3181308 0.3339218 0.3345335 0.3365828
#> [58,] 0.3878878 0.4434012 0.4459895 0.4483702 0.4940362 0.5446174 0.5545050
#> [59,] 0.4580175 0.4767503 0.4962972 0.5153071 0.5604105 0.5629230 0.5730672
#> [60,] 0.2918292 0.3089694 0.3404541 0.3896341 0.4101332 0.4653608 0.4695010
#> [61,] 0.3037445 0.3208846 0.3523694 0.3777189 0.3982180 0.4534455 0.4575858
#> [62,] 0.2610205 0.3344099 0.3684878 0.3769126 0.4657202 0.4794951 0.5011494
#> [63,] 0.2615177 0.2772313 0.2852972 0.2917108 0.3379606 0.3720385 0.4578170
#> [64,] 0.3661367 0.3696586 0.4349338 0.4682558 0.5637136 0.5640429 0.5660939
#> [65,] 0.2921115 0.4305159 0.4369294 0.4449954 0.4570824 0.4607090 0.4615847
#> [66,] 0.3959938 0.3977770 0.4243636 0.4438434 0.4528982 0.4551255 0.4595570
#> [67,] 0.3340971 0.3560276 0.3584530 0.3681328 0.3735612 0.4068192 0.4141292
#> [68,] 0.2692031 0.3048635 0.3182108 0.3281957 0.3644590 0.3948539 0.3963717
#> [69,] 0.3551585 0.3615720 0.3674689 0.3696380 0.3853516 0.4314179 0.4332012
#> [70,] 0.3493045 0.3566530 0.3778243 0.3858634 0.3919040 0.4014230 0.4227696
#> [71,] 0.2995101 0.3551141 0.3574080 0.3591854 0.4751788 0.5104342 0.5717452
#> [72,] 0.2602411 0.2836240 0.3142153 0.3142171 0.3300081 0.3306198 0.3404965
#> [73,] 0.2224456 0.2369554 0.2535253 0.2757574 0.2831069 0.3291594 0.3504743
#> [74,] 0.4529932 0.4612169 0.4614671 0.4688166 0.4910487 0.5029120 0.5044298
#> [75,] 0.3272620 0.3295180 0.3390369 0.4053691 0.4073401 0.4149897 0.4190391
#> [76,] 0.2879060 0.2895408 0.3046825 0.3067943 0.3140436 0.3397411 0.3721027
#> [77,] 0.2067764 0.2189794 0.2233463 0.2455784 0.2529279 0.3593384 0.3806533
#> [78,] 0.2440910 0.2692122 0.2733524 0.3285800 0.3490791 0.3598424 0.3881593
#> [79,] 0.2918451 0.2930446 0.2968141 0.3020900 0.3093107 0.3278743 0.3758577
#> [80,] 0.2434031 0.2776743 0.3195571 0.3290151 0.3435038 0.3531244 0.3592918
#> [81,] 0.2012035 0.2754682 0.3642758 0.3780506 0.4074470 0.4147475 0.4358544
#> [82,] 0.3042797 0.3129221 0.3223614 0.3337229 0.3720350 0.3730434 0.3942241
#> [83,] 0.2394589 0.2488982 0.2602597 0.2932461 0.3980482 0.4454982 0.4465066
#> [84,] 0.2255428 0.2563514 0.2836019 0.2906313 0.2946631 0.3171154 0.3312480
#> [85,] 0.3426330 0.3931623 0.4079082 0.4952814 0.5366880 0.5630851 0.5833264
#> [86,] 0.2205470 0.2931679 0.3176392 0.3240921 0.3264259 0.3300467 0.3318544
#> [87,] 0.2665734 0.2822870 0.2903530 0.2967665 0.3329049 0.3669828 0.4628727
#> [88,] 0.3141724 0.3217475 0.3566635 0.4034121 0.4037315 0.4211674 0.4574015
#> [89,] 0.2011333 0.2124948 0.2662948 0.3410109 0.3502833 0.4229923 0.4910795
#> [90,] 0.3845538 0.3863371 0.4324034 0.4358036 0.4481170 0.4561830 0.4625965
#> [91,] 0.1909763 0.2242342 0.2310910 0.2696478 0.3529510 0.3696481 0.3884507
#> [92,] 0.2467879 0.2742353 0.2772720 0.2872003 0.3060029 0.3227000 0.4514168
#> [93,] 0.2655857 0.2979195 0.2997027 0.3010101 0.3030611 0.3244726 0.3389823
#> [94,] 0.2973275 0.3529315 0.3552253 0.3570028 0.4729962 0.5082516 0.5695625
#> [95,] 0.2640570 0.2929153 0.3347317 0.3515083 0.3536200 0.3608693 0.4189284
#> [96,] 0.2409253 0.3545051 0.3568175 0.3885829 0.4456251 0.4593999 0.4887963
#> [97,] 0.3431753 0.3495888 0.3576548 0.3733684 0.3794521 0.4194347 0.4212180
#> [98,] 0.2997070 0.3363925 0.4646779 0.4651724 0.4915695 0.5118108 0.5420874
#> [99,] 0.2435438 0.2552587 0.2818674 0.2970097 0.3309071 0.3438129 0.3542066
#> [100,] 0.3456993 0.3457214 0.3562410 0.3733811 0.4009490 0.4048659 0.4050893
#> [101,] 0.1675306 0.2549925 0.2963104 0.3277015 0.3615857 0.3957887 0.4013887
#> [102,] 0.2341797 0.2828068 0.3090880 0.3150325 0.3199604 0.3456256 0.3614166
#> [103,] 0.2512348 0.2657517 0.2775160 0.2883884 0.3466045 0.3501805 0.3771976
#> [104,] 0.3299451 0.3363981 0.3380837 0.3436837 0.4117709 0.4334902 0.4410653
#> [105,] 0.4393521 0.4396136 0.4895524 0.5123245 0.5539369 0.5695073 0.5729310
#> [106,] 0.2693322 0.2700609 0.2822973 0.2893033 0.2924493 0.3025936 0.3097447
#> [107,] 0.1880655 0.2886063 0.3774138 0.3911887 0.4205851 0.4227163 0.4278856
#> [108,] 0.3196626 0.3368028 0.3618007 0.3682875 0.3822998 0.4375274 0.4416676
#> [109,] 0.3134157 0.3246575 0.3247771 0.3342165 0.3428588 0.3548334 0.4043677
#> [110,] 0.3633285 0.3859780 0.4118433 0.4139096 0.4845844 0.5013609 0.5034726
#> [111,] 0.3646600 0.3661575 0.3707006 0.3778564 0.3802196 0.3990277 0.4439729
#> [112,] 0.2721101 0.3170553 0.3445027 0.3574678 0.3762704 0.3929675 0.4097161
#> [113,] 0.2816346 0.2987748 0.3302595 0.3998287 0.4203278 0.4755554 0.4796956
#> [114,] 0.2554064 0.3143825 0.3784958 0.3916715 0.3966708 0.4057161 0.4129369
#> [115,] 0.3887954 0.4443994 0.4466933 0.4484707 0.5644641 0.5997195 0.6610305
#> [116,] 0.3218298 0.3774337 0.3797276 0.3815050 0.4974984 0.5327538 0.5940648
#> [117,] 0.3761689 0.3870293 0.4617454 0.4719561 0.4740070 0.5094314 0.5265698
#> [118,] 0.2053691 0.2203867 0.2219390 0.2441711 0.2515206 0.3607457 0.3820606
#> [119,] 0.2022721 0.2112423 0.2675473 0.3422635 0.3490308 0.4217398 0.4898270
#> [120,] 0.1958307 0.1962097 0.1999709 0.2551985 0.2756976 0.4160565 0.4332238
#> [121,] 0.2444372 0.2538952 0.2743432 0.2841719 0.2917791 0.3044131 0.3308102
#> [122,] 0.2791887 0.2878310 0.2972703 0.3086318 0.3971260 0.3981345 0.4193152
#> [123,] 0.2610780 0.2953492 0.3258289 0.3354495 0.3372320 0.3466900 0.3769666
#> [124,] 0.3161257 0.3221220 0.3523598 0.3579598 0.4192141 0.4260470 0.4267892
#> [125,] 0.3280096 0.3787237 0.3807746 0.4161990 0.4333375 0.4546523 0.4802617
#> [126,] 0.2801751 0.2882393 0.3014900 0.4418489 0.4589828 0.4623480 0.4801635
#> [127,] 0.2603386 0.2676390 0.2751020 0.2854958 0.2970355 0.3108103 0.3204858
#> [128,] 0.2942442 0.3595194 0.4415511 0.4882992 0.5146963 0.5349376 0.5436702
#> [129,] 0.2761385 0.2918521 0.2999180 0.3063315 0.3233399 0.3574177 0.4724377
#> [130,] 0.2512081 0.2572675 0.2578792 0.2584574 0.2605691 0.2736702 0.2773457
#> [131,] 0.3334677 0.3362486 0.3526833 0.3613698 0.3987090 0.4145400 0.4250817
#> [132,] 0.3505313 0.3581064 0.3673726 0.3848085 0.3930224 0.4210425 0.4266426
#> [133,] 0.3248705 0.3492264 0.3589062 0.3643346 0.3652542 0.3975926 0.4233559
#> [134,] 0.4559534 0.4616080 0.4623900 0.4781779 0.4824338 0.4906576 0.4926876
#> [135,] 0.2869621 0.4345300 0.4390323 0.4452146 0.4530683 0.4594818 0.4644302
#> [136,] 0.2910525 0.3043780 0.3384558 0.4069446 0.4711175 0.4910318 0.4957522
#> [137,] 0.2437757 0.2780469 0.3199297 0.3293877 0.3431312 0.3527518 0.3596644
#> [138,] 0.3817470 0.3864490 0.4949645 0.5029417 0.5079107 0.5535767 0.6041579
#> [139,] 0.2485606 0.2602756 0.2868843 0.3020265 0.3258902 0.3488297 0.3592235
#> [140,] 0.2218400 0.2239069 0.2552553 0.2751697 0.3879463 0.4078314 0.4252854
#> [141,] 0.3415996 0.3798925 0.3843948 0.3905770 0.4097926 0.4716493 0.4821910
#> [142,] 0.1977638 0.2595559 0.2598099 0.2950653 0.3125620 0.3337980 0.3563763
#> [143,] 0.3963399 0.4519438 0.4542377 0.4560151 0.5720085 0.6072639 0.6685749
#> [144,] 0.3307293 0.3722669 0.4557079 0.4685179 0.4777410 0.4798793 0.4836957
#> [145,] 0.3922731 0.4866927 0.5065963 0.5221668 0.5368930 0.5596651 0.5865195
#> [146,] 0.2059988 0.2197570 0.2225687 0.2448008 0.2521503 0.3601159 0.3814308
#> [147,] 0.2721076 0.2734185 0.2789396 0.2981821 0.3008659 0.3013281 0.3114723
#> [148,] 0.3690173 0.4833406 0.4989110 0.5099485 0.5601488 0.5632637 0.5829208
#> [149,] 0.2925717 0.3455015 0.3568630 0.3663023 0.3749446 0.3869193 0.4364535
#> [150,] 0.4562310 0.4613304 0.4677670 0.4728009 0.4873106 0.4878109 0.4960346
#> [151,] 0.1947594 0.2404852 0.2453065 0.3024379 0.3096592 0.3252296 0.3491865
#> [152,] 0.2301448 0.2337538 0.2602379 0.2672673 0.3109977 0.3253264 0.3325758
#> [153,] 0.3395816 0.3580977 0.3901287 0.4144845 0.4241643 0.4295928 0.4628507
#> [154,] 0.2411370 0.2413933 0.2494592 0.2558727 0.3737987 0.4078765 0.4219789
#> [155,] 0.2098254 0.2126977 0.2854067 0.3386053 0.3534939 0.3590939 0.3953280
#> [156,] 0.3539818 0.3798471 0.3953246 0.4459058 0.4865994 0.5165806 0.5333571
#> [157,] 0.3329890 0.3973418 0.4070898 0.4329551 0.4478888 0.4722447 0.4819244
#> [158,] 0.2467531 0.2624667 0.2705326 0.2769461 0.3527253 0.3868031 0.4430523
#> [159,] 0.3347181 0.3940166 0.4836715 0.4850743 0.4913191 0.5015004 0.6305993
#> [160,] 0.2972077 0.3067256 0.3255247 0.3318468 0.3359870 0.3424667 0.3738152
#> [161,] 0.3440925 0.3782587 0.3797530 0.3839112 0.3981731 0.4295216 0.4464636
#> [162,] 0.2406345 0.2536990 0.2825173 0.2919753 0.3222519 0.3424932 0.3688903
#> [163,] 0.2632395 0.2663855 0.2765297 0.2765934 0.2953961 0.3083611 0.3241456
#> [164,] 0.3384912 0.3682421 0.3702930 0.4057174 0.4228559 0.4441708 0.4907433
#> [165,] 0.2537701 0.2639143 0.2725118 0.2892088 0.3080115 0.3115302 0.3209765
#> [166,] 0.2875438 0.3468423 0.4364972 0.4379000 0.4441448 0.4543260 0.5834249
#> [167,] 0.3549063 0.4692295 0.4848000 0.5240595 0.5491527 0.5742598 0.5970318
#> [168,] 0.3092310 0.3268685 0.4556484 0.4742019 0.4820455 0.5022868 0.5325634
#> [169,] 0.2713032 0.2815601 0.2836110 0.3173695 0.3191528 0.3439227 0.3584324
#> [170,] 0.3167221 0.3809572 0.4234743 0.4315043 0.4493396 0.4558601 0.4655399
#> [171,] 0.1905947 0.2238526 0.2314726 0.2700294 0.3525694 0.3692665 0.3880691
#> [172,] 0.3134519 0.3640330 0.4347078 0.4358546 0.4514843 0.4535961 0.4608454
#> [173,] 0.3036087 0.4190187 0.4254322 0.4334981 0.4492117 0.4685796 0.4730819
#> [174,] 0.3438697 0.3750638 0.3752182 0.3921602 0.3983960 0.4204771 0.4340564
#> [175,] 0.3428465 0.3446298 0.3906962 0.4064098 0.4144757 0.4208892 0.4775109
#> [176,] 0.2333419 0.2609915 0.3028744 0.3123324 0.3426090 0.3601865 0.3628502
#> [177,] 0.2673857 0.2720121 0.2728142 0.2795872 0.2824940 0.3068498 0.3573969
#> [178,] 0.2618985 0.2687203 0.2828529 0.3093371 0.3163665 0.3232095 0.3584649
#> [179,] 0.2315991 0.2370211 0.2516430 0.2580796 0.3661200 0.3763012 0.3803713
#> [180,] 0.2936296 0.3016956 0.3174092 0.3332921 0.3634755 0.3652588 0.3900287
#> [181,] 0.2614875 0.2954848 0.3321622 0.3489388 0.3510505 0.3582998 0.4163589
#> [182,] 0.2270498 0.2544972 0.2674622 0.2862649 0.2970101 0.3029619 0.4316787
#> [183,] 0.3411842 0.3725326 0.3777493 0.3894747 0.4010815 0.4177916 0.4367419
#> [184,] 0.2093214 0.2147499 0.2458742 0.2480078 0.3767246 0.3934217 0.4063234
#> [185,] 0.2813221 0.4413053 0.4462930 0.4477188 0.4507954 0.4557847 0.4569776
#> [186,] 0.2514034 0.2707410 0.2963487 0.3175200 0.3215701 0.3284021 0.3292189
#> [187,] 0.2711797 0.3161249 0.3435723 0.3565374 0.3753400 0.3920371 0.4106465
#> [188,] 0.4380882 0.4573307 0.4641627 0.4975528 0.5149918 0.5358645 0.5721149
#> [189,] 0.1930388 0.2126747 0.2731170 0.2770274 0.2925978 0.3350697 0.3818183
#> [190,] 0.3403933 0.3448956 0.4199837 0.4463808 0.4666221 0.4968987 0.5063567
#> [191,] 0.3062489 0.3138240 0.3487400 0.3954886 0.4116549 0.4290909 0.4574413
#> [192,] 0.2785825 0.3594907 0.3708522 0.3802915 0.3889339 0.4009085 0.4504427
#> [193,] 0.2593498 0.2597886 0.2604003 0.2774406 0.2942326 0.3183860 0.3304605
#> [194,] 0.2951544 0.2997567 0.3166988 0.3324935 0.3480472 0.3576147 0.3617550
#> [195,] 0.2135527 0.2748636 0.3101191 0.3170662 0.3311988 0.3576830 0.3647124
#> [196,] 0.2418885 0.2718265 0.3050845 0.3105130 0.3201927 0.3389806 0.3445486
#> [197,] 0.3740482 0.3891500 0.4487644 0.4849371 0.4869881 0.5140396 0.5224125
#> [198,] 0.3509919 0.3557413 0.3577923 0.3932167 0.4103551 0.4316700 0.5032440
#> [199,] 0.2262359 0.2283652 0.2301426 0.2474718 0.3461360 0.3813915 0.4427024
#> [200,] 0.2887854 0.3540606 0.4470099 0.4828404 0.5092376 0.5294788 0.5491290
#> [,20]
#> [1,] 0.6411620
#> [2,] 0.6793907
#> [3,] 0.3854130
#> [4,] 0.4961456
#> [5,] 0.4482501
#> [6,] 0.4448531
#> [7,] 0.3401498
#> [8,] 0.5542353
#> [9,] 0.3534801
#> [10,] 0.3790349
#> [11,] 0.4191325
#> [12,] 0.3665117
#> [13,] 0.3668104
#> [14,] 0.5125302
#> [15,] 0.5165523
#> [16,] 0.6400157
#> [17,] 0.3956872
#> [18,] 0.3452617
#> [19,] 0.4246012
#> [20,] 0.3566397
#> [21,] 0.5640625
#> [22,] 0.3335814
#> [23,] 0.4523496
#> [24,] 0.7528144
#> [25,] 0.3294781
#> [26,] 0.3477425
#> [27,] 0.3205647
#> [28,] 0.3672544
#> [29,] 0.3727889
#> [30,] 0.4939103
#> [31,] 0.4710914
#> [32,] 0.4327903
#> [33,] 0.3831010
#> [34,] 0.5336663
#> [35,] 0.4599674
#> [36,] 0.4827637
#> [37,] 0.5546456
#> [38,] 0.3519100
#> [39,] 0.4520601
#> [40,] 0.4632787
#> [41,] 0.3911497
#> [42,] 0.3987174
#> [43,] 0.4873326
#> [44,] 0.4650493
#> [45,] 0.4041262
#> [46,] 0.3911854
#> [47,] 0.3805382
#> [48,] 0.3905441
#> [49,] 0.4103551
#> [50,] 0.6052413
#> [51,] 0.4341248
#> [52,] 0.4011462
#> [53,] 0.3446794
#> [54,] 0.4771297
#> [55,] 0.3414477
#> [56,] 0.3375328
#> [57,] 0.3474552
#> [58,] 0.6152921
#> [59,] 0.5762132
#> [60,] 0.4946222
#> [61,] 0.4827070
#> [62,] 0.5088915
#> [63,] 0.4951561
#> [64,] 0.5901107
#> [65,] 0.4677670
#> [66,] 0.4676230
#> [67,] 0.5208815
#> [68,] 0.4252981
#> [69,] 0.4579711
#> [70,] 0.4502170
#> [71,] 0.6525980
#> [72,] 0.3476600
#> [73,] 0.3676127
#> [74,] 0.5076186
#> [75,] 0.4402103
#> [76,] 0.3791321
#> [77,] 0.3977917
#> [78,] 0.4051013
#> [79,] 0.3926498
#> [80,] 0.3795330
#> [81,] 0.4469506
#> [82,] 0.4715114
#> [83,] 0.4676873
#> [84,] 0.3552696
#> [85,] 0.5910685
#> [86,] 0.3415341
#> [87,] 0.5002119
#> [88,] 0.4630015
#> [89,] 0.4932631
#> [90,] 0.4643382
#> [91,] 0.4014158
#> [92,] 0.4799836
#> [93,] 0.3555522
#> [94,] 0.6504154
#> [95,] 0.4259579
#> [96,] 0.4960968
#> [97,] 0.4459879
#> [98,] 0.5515454
#> [99,] 0.3891966
#> [100,] 0.4302105
#> [101,] 0.4363018
#> [102,] 0.3620283
#> [103,] 0.3929886
#> [104,] 0.4759813
#> [105,] 0.6112426
#> [106,] 0.3502094
#> [107,] 0.4567942
#> [108,] 0.4667888
#> [109,] 0.4356232
#> [110,] 0.5107220
#> [111,] 0.4465518
#> [112,] 0.4550188
#> [113,] 0.5010031
#> [114,] 0.4167756
#> [115,] 0.7418833
#> [116,] 0.6749177
#> [117,] 0.5270206
#> [118,] 0.3991990
#> [119,] 0.4945156
#> [120,] 0.4373714
#> [121,] 0.4186237
#> [122,] 0.4464203
#> [123,] 0.3972079
#> [124,] 0.4617052
#> [125,] 0.5549778
#> [126,] 0.4811719
#> [127,] 0.3788122
#> [128,] 0.5652142
#> [129,] 0.5097769
#> [130,] 0.3042632
#> [131,] 0.4422218
#> [132,] 0.4397710
#> [133,] 0.5263094
#> [134,] 0.5174575
#> [135,] 0.4675478
#> [136,] 0.5095270
#> [137,] 0.3799056
#> [138,] 0.6554137
#> [139,] 0.3942134
#> [140,] 0.4419092
#> [141,] 0.4993311
#> [142,] 0.4372291
#> [143,] 0.7494278
#> [144,] 0.4893187
#> [145,] 0.6202715
#> [146,] 0.3985693
#> [147,] 0.3458112
#> [148,] 0.6138108
#> [149,] 0.4677091
#> [150,] 0.5120805
#> [151,] 0.3841026
#> [152,] 0.3346875
#> [153,] 0.4648499
#> [154,] 0.4593181
#> [155,] 0.4038805
#> [156,] 0.5354688
#> [157,] 0.4873529
#> [158,] 0.4803915
#> [159,] 0.6628024
#> [160,] 0.3912146
#> [161,] 0.4747806
#> [162,] 0.3805436
#> [163,] 0.3358085
#> [164,] 0.5654594
#> [165,] 0.3484239
#> [166,] 0.6156281
#> [167,] 0.5996997
#> [168,] 0.5420214
#> [169,] 0.3750023
#> [170,] 0.4709684
#> [171,] 0.4010342
#> [172,] 0.4617199
#> [173,] 0.4792642
#> [174,] 0.4382146
#> [175,] 0.5060455
#> [176,] 0.3698072
#> [177,] 0.3766793
#> [178,] 0.3744256
#> [179,] 0.3825460
#> [180,] 0.4045384
#> [181,] 0.4233883
#> [182,] 0.4649367
#> [183,] 0.4409001
#> [184,] 0.4122244
#> [185,] 0.4714983
#> [186,] 0.3476446
#> [187,] 0.4559492
#> [188,] 0.5927587
#> [189,] 0.4069211
#> [190,] 0.5098666
#> [191,] 0.4653249
#> [192,] 0.4812940
#> [193,] 0.3422160
#> [194,] 0.3679616
#> [195,] 0.4227715
#> [196,] 0.3454335
#> [197,] 0.5395509
#> [198,] 0.5720290
#> [199,] 0.5235553
#> [200,] 0.5597554
#>