data: Generating Survival Data from Log-normal AFT Model
In imputeYn: Imputing the Last Largest Censored Observation(s) Under Weighted Least Squares
Description
Usage
Arguments
Details
Value
Author(s)
References
Examples
Description
This gives the survival data generated from log-normal AFT model.
Usage
1
data(n, p, r, b1, sig, Cper)
Arguments
n
sample size.
p
the number of covariates. For the AFT model each covariate is generated from Uniform(0, 1) distribution
r
correlation between the covariates, r is set to 0 for no correlation.
b1
the vector of coefficients.
sig
this maintains noise ratio, 1 for no noise.
Cper
takes specific value for generating specific censoring percentage, e.g., -0.2 for 30 censoring percentage, 0.0 for 50 censoring percentage and 0.2 for 70 percentages.
Details
Generate survival data from a log-normal AFT model (Y = alpha + X (beta) + error; Y=log(T)) where error is N(0,1). The last largest datum is generated always as censored otherwise censorship is random with censoring time generated from Uniform (c, 2c) for a suitable c.
Value
y
logarithmic of survival time
x
matrix of covariates of order n by p
delta
status; 1 for uncensored, o for censored
Pper
censoring percentage
Author(s)
Hasinur Rahaman Khan and Ewart Shaw
References
Khan and Shaw. (2013a). On Dealing with Censored Largest Observations under Weighted Least Squares. CRiSM working paper, Department of Statistics, University of Warwick, UK, No. 13-07. Also available in http://arxiv.org/abs/1312.2533.
Examples
1
2
3
4
5
6
7
8
9
#Dataset with zero correlation between the covariates and the medium censoring level
#(50 percent)
data1<-data(n=100, p=2, r=0, b1=c(2,4), sig=1, Cper=0)
data1
#Dataset with moderate correlation between the covariates and the higher censoring level
#(70 percent)
data.r<-data(n=100, p=2, r=0.5, b1=c(2,4), sig=1, Cper=0.2)
data.r
Example output
Loading required package: quadprog
Loading required package: emplik
Loading required package: mvtnorm
Loading required package: survival
Loading required package: boot
Attaching package: ‘boot’
The following object is masked from ‘package:survival’:
aml
Attaching package: ‘imputeYn’
The following object is masked from ‘package:utils’:
data
$y
[,1]
[1,] -1.490596e+00
[2,] -1.448699e+00
[3,] -1.304946e+00
[4,] -1.140452e+00
[5,] -1.024939e+00
[6,] -1.016997e+00
[7,] -9.061287e-01
[8,] -8.775528e-01
[9,] -5.402613e-01
[10,] -4.510826e-01
[11,] -4.492635e-01
[12,] -3.202873e-01
[13,] -1.695147e-01
[14,] -1.368129e-01
[15,] -3.446866e-02
[16,] -7.969948e-05
[17,] 2.551893e-02
[18,] 1.327122e-01
[19,] 1.872044e-01
[20,] 2.215430e-01
[21,] 2.749025e-01
[22,] 2.842287e-01
[23,] 3.656798e-01
[24,] 3.926379e-01
[25,] 5.144067e-01
[26,] 5.843210e-01
[27,] 6.252607e-01
[28,] 6.978630e-01
[29,] 7.115890e-01
[30,] 7.275057e-01
[31,] 7.654093e-01
[32,] 9.580971e-01
[33,] 9.648227e-01
[34,] 1.032831e+00
[35,] 1.040238e+00
[36,] 1.109877e+00
[37,] 1.154714e+00
[38,] 1.187994e+00
[39,] 1.212367e+00
[40,] 1.314550e+00
[41,] 1.339962e+00
[42,] 1.362065e+00
[43,] 1.410882e+00
[44,] 1.490646e+00
[45,] 1.513951e+00
[46,] 1.580968e+00
[47,] 1.859841e+00
[48,] 1.887315e+00
[49,] 1.904084e+00
[50,] 1.985168e+00
[51,] 2.051422e+00
[52,] 2.094406e+00
[53,] 2.097436e+00
[54,] 2.133348e+00
[55,] 2.137555e+00
[56,] 2.159415e+00
[57,] 2.166578e+00
[58,] 2.197953e+00
[59,] 2.205251e+00
[60,] 2.213610e+00
[61,] 2.268682e+00
[62,] 2.358280e+00
[63,] 2.401979e+00
[64,] 2.425581e+00
[65,] 2.489497e+00
[66,] 2.518313e+00
[67,] 2.594513e+00
[68,] 2.609954e+00
[69,] 2.621219e+00
[70,] 2.629718e+00
[71,] 2.686806e+00
[72,] 2.887496e+00
[73,] 2.892745e+00
[74,] 2.922870e+00
[75,] 2.950506e+00
[76,] 3.092064e+00
[77,] 3.141766e+00
[78,] 3.193537e+00
[79,] 3.209344e+00
[80,] 3.297576e+00
[81,] 3.420199e+00
[82,] 3.439402e+00
[83,] 3.441932e+00
[84,] 3.444023e+00
[85,] 3.697358e+00
[86,] 3.898381e+00
[87,] 4.070555e+00
[88,] 4.112334e+00
[89,] 4.137917e+00
[90,] 4.193426e+00
[91,] 4.406721e+00
[92,] 4.440835e+00
[93,] 4.499303e+00
[94,] 4.718543e+00
[95,] 4.914510e+00
[96,] 5.036963e+00
[97,] 5.207800e+00
[98,] 5.476322e+00
[99,] 5.517171e+00
[100,] 6.483557e+00
$x
[,1] [,2]
[1,] 0.008285618 0.02004632
[2,] 0.603948027 0.04136400
[3,] 0.749886048 0.80537665
[4,] 0.268061888 0.64785515
[5,] 0.579744524 0.85515809
[6,] 0.670466864 0.88070744
[7,] 0.039840392 0.01954896
[8,] 0.305548955 0.72960546
[9,] 0.359227001 0.89164752
[10,] 0.689658555 0.54660851
[11,] 0.754070207 0.85070181
[12,] 0.800294591 0.54280922
[13,] 0.074289950 0.26769015
[14,] 0.239568133 0.97094194
[15,] 0.622065050 0.06828453
[16,] 0.727132641 0.27365789
[17,] 0.546636574 0.80279058
[18,] 0.802719830 0.31456396
[19,] 0.609042065 0.15779918
[20,] 0.819738729 0.27085236
[21,] 0.680980340 0.71784881
[22,] 0.868506235 0.66708590
[23,] 0.735999623 0.04362489
[24,] 0.140612081 0.17409860
[25,] 0.577776826 0.52482366
[26,] 0.986593809 0.13743821
[27,] 0.217697633 0.58492996
[28,] 0.238560191 0.18250626
[29,] 0.580880128 0.74624072
[30,] 0.382228391 0.77651939
[31,] 0.954001454 0.08329257
[32,] 0.229965508 0.85957270
[33,] 0.693629754 0.85071214
[34,] 0.373688609 0.16757145
[35,] 0.546343721 0.40440447
[36,] 0.265669918 0.23879413
[37,] 0.642581882 0.20311241
[38,] 0.732441386 0.58364495
[39,] 0.741724879 0.84501602
[40,] 0.281390808 0.87511534
[41,] 0.163431903 0.04918670
[42,] 0.104867396 0.13198850
[43,] 0.744740272 0.81764503
[44,] 0.131073454 0.90196323
[45,] 0.365897471 0.48585119
[46,] 0.184721524 0.62539224
[47,] 0.048235682 0.33119733
[48,] 0.123359561 0.02005913
[49,] 0.950732729 0.16068665
[50,] 0.368947438 0.46759172
[51,] 0.288823119 0.91767980
[52,] 0.381344867 0.19854325
[53,] 0.788756985 0.71178541
[54,] 0.392592578 0.26727408
[55,] 0.450617155 0.56031002
[56,] 0.110833225 0.76217824
[57,] 0.775727746 0.36956189
[58,] 0.401736462 0.33824809
[59,] 0.798350696 0.68388506
[60,] 0.849601799 0.86007808
[61,] 0.029630458 0.84507010
[62,] 0.114465718 0.51968629
[63,] 0.530401196 0.10902959
[64,] 0.456595083 0.77547613
[65,] 0.085689292 0.32625308
[66,] 0.975080423 0.39024683
[67,] 0.241971032 0.74734415
[68,] 0.696059793 0.84045058
[69,] 0.541718748 0.11816538
[70,] 0.396946717 0.17927819
[71,] 0.301907460 0.64145860
[72,] 0.238763664 0.82567239
[73,] 0.155480494 0.85043632
[74,] 0.468320030 0.20160606
[75,] 0.365256759 0.51141369
[76,] 0.793021146 0.36135729
[77,] 0.887595445 0.82627047
[78,] 0.942793358 0.71578495
[79,] 0.829833405 0.28091666
[80,] 0.610367620 0.60225763
[81,] 0.574682808 0.70943990
[82,] 0.238297680 0.90659999
[83,] 0.991291813 0.14671926
[84,] 0.007570231 0.76349598
[85,] 0.953918792 0.61001960
[86,] 0.730642145 0.70180084
[87,] 0.360288379 0.24620897
[88,] 0.134702833 0.69867497
[89,] 0.229572109 0.96540188
[90,] 0.562822985 0.79569573
[91,] 0.458305422 0.57656953
[92,] 0.191316289 0.82916908
[93,] 0.935334133 0.65727461
[94,] 0.302043875 0.95929916
[95,] 0.682437687 0.83224093
[96,] 0.370492648 0.96043441
[97,] 0.988907159 0.55368815
[98,] 0.833822708 0.87356512
[99,] 0.617153703 0.69374266
[100,] 0.662917295 0.95184023
$delta
[,1]
[1,] 1
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 1
[8,] 0
[9,] 0
[10,] 0
[11,] 0
[12,] 0
[13,] 0
[14,] 0
[15,] 1
[16,] 0
[17,] 0
[18,] 0
[19,] 1
[20,] 0
[21,] 0
[22,] 0
[23,] 0
[24,] 1
[25,] 0
[26,] 1
[27,] 1
[28,] 1
[29,] 0
[30,] 0
[31,] 0
[32,] 0
[33,] 0
[34,] 1
[35,] 1
[36,] 0
[37,] 0
[38,] 0
[39,] 0
[40,] 0
[41,] 1
[42,] 1
[43,] 0
[44,] 0
[45,] 0
[46,] 1
[47,] 1
[48,] 1
[49,] 1
[50,] 1
[51,] 0
[52,] 1
[53,] 0
[54,] 1
[55,] 1
[56,] 0
[57,] 0
[58,] 1
[59,] 0
[60,] 0
[61,] 1
[62,] 1
[63,] 1
[64,] 0
[65,] 1
[66,] 1
[67,] 0
[68,] 1
[69,] 1
[70,] 1
[71,] 1
[72,] 0
[73,] 0
[74,] 0
[75,] 0
[76,] 1
[77,] 1
[78,] 0
[79,] 1
[80,] 1
[81,] 1
[82,] 1
[83,] 1
[84,] 1
[85,] 1
[86,] 1
[87,] 1
[88,] 0
[89,] 0
[90,] 1
[91,] 1
[92,] 1
[93,] 1
[94,] 1
[95,] 1
[96,] 0
[97,] 1
[98,] 1
[99,] 1
[100,] 0
$Pper
[1] 50
$y
[,1]
[1,] -2.00081900
[2,] -1.98977696
[3,] -1.91927836
[4,] -1.82132514
[5,] -1.81987482
[6,] -1.73135488
[7,] -1.70653544
[8,] -1.62619379
[9,] -1.53584099
[10,] -1.39643230
[11,] -1.35130805
[12,] -1.30206533
[13,] -1.10592834
[14,] -0.74818002
[15,] -0.71102154
[16,] -0.59785034
[17,] -0.53070726
[18,] -0.51914616
[19,] -0.50289238
[20,] -0.44960559
[21,] -0.37325844
[22,] -0.31597869
[23,] -0.23623907
[24,] -0.07280976
[25,] -0.02442669
[26,] 0.03201953
[27,] 0.11599098
[28,] 0.12120679
[29,] 0.26608613
[30,] 0.31738677
[31,] 0.45064416
[32,] 0.52609660
[33,] 0.60190508
[34,] 0.61166043
[35,] 0.62186342
[36,] 0.63834095
[37,] 0.68220696
[38,] 0.86093913
[39,] 0.96055285
[40,] 1.03521196
[41,] 1.05558807
[42,] 1.24675233
[43,] 1.25380151
[44,] 1.43329805
[45,] 1.47717516
[46,] 1.48523742
[47,] 1.53953695
[48,] 1.56063522
[49,] 1.60393899
[50,] 1.65433458
[51,] 1.75532586
[52,] 1.83577334
[53,] 1.95271068
[54,] 2.05814127
[55,] 2.16348011
[56,] 2.29160458
[57,] 2.32457594
[58,] 2.34099761
[59,] 2.34982427
[60,] 2.45528632
[61,] 2.46239813
[62,] 2.51206258
[63,] 2.51480409
[64,] 2.60656767
[65,] 2.62068979
[66,] 2.68083623
[67,] 2.69643942
[68,] 2.70609530
[69,] 2.80432824
[70,] 2.90916822
[71,] 2.95498018
[72,] 2.95759585
[73,] 3.11129235
[74,] 3.11361063
[75,] 3.13801746
[76,] 3.37782138
[77,] 3.44313182
[78,] 3.54419455
[79,] 3.74833287
[80,] 3.74891717
[81,] 3.76361732
[82,] 3.80347343
[83,] 3.80911363
[84,] 3.82294230
[85,] 3.99019448
[86,] 4.01551187
[87,] 4.01983148
[88,] 4.16078641
[89,] 4.22717421
[90,] 4.40605029
[91,] 4.51652742
[92,] 4.52271285
[93,] 4.67712870
[94,] 4.70094896
[95,] 4.84780957
[96,] 4.85870941
[97,] 5.68137551
[98,] 5.83957891
[99,] 6.01000953
[100,] 6.01821177
$x
[,1] [,2]
[1,] 0.104132310 0.39267084
[2,] 0.732147299 1.18388207
[3,] 0.494005437 0.78034102
[4,] 0.990595904 0.82871002
[5,] 0.719762678 1.19623833
[6,] 0.158678906 0.92518932
[7,] 0.566521263 1.11380322
[8,] 0.831944648 0.91772891
[9,] 0.884370878 0.84801319
[10,] 0.275581250 0.47080631
[11,] 0.003151742 0.03846625
[12,] 0.912079474 0.55724741
[13,] 0.213539267 0.14151800
[14,] 0.383799729 0.27736820
[15,] 0.063233601 0.48986771
[16,] 0.603731662 0.52202852
[17,] 0.307617045 0.95416328
[18,] 0.929436242 0.83831423
[19,] 0.275955417 0.84540988
[20,] 0.156036330 0.19330358
[21,] 0.091499316 0.13796514
[22,] 0.150722792 0.16498462
[23,] 0.861986283 1.06960639
[24,] 0.239624630 0.96234059
[25,] 0.675493272 0.74051085
[26,] 0.357627908 0.76020211
[27,] 0.481756836 0.64825763
[28,] 0.383551049 0.82472182
[29,] 0.135659873 0.48920981
[30,] 0.484105288 0.48590694
[31,] 0.959735574 0.57941609
[32,] 0.414090431 1.03918724
[33,] 0.087663108 0.51947066
[34,] 0.615063014 0.69619659
[35,] 0.259916195 0.32924257
[36,] 0.148873104 0.76089358
[37,] 0.284802383 0.64342799
[38,] 0.775593658 1.13242453
[39,] 0.785706502 0.57509340
[40,] 0.397226878 0.32797422
[41,] 0.505933467 0.32774330
[42,] 0.224558837 0.89003381
[43,] 0.593637761 1.07230537
[44,] 0.291767699 0.26578603
[45,] 0.097319045 0.80863128
[46,] 0.960398150 0.98899906
[47,] 0.739743918 0.41327425
[48,] 0.577929757 0.62203579
[49,] 0.020161122 0.38388413
[50,] 0.272938660 0.21225485
[51,] 0.320465329 0.19205163
[52,] 0.577300053 0.47703343
[53,] 0.096317067 0.20605126
[54,] 0.506448317 1.09418243
[55,] 0.136715003 0.27729313
[56,] 0.757482575 0.70590554
[57,] 0.537896304 0.43256712
[58,] 0.631669580 1.04709937
[59,] 0.623746094 0.66542269
[60,] 0.779742509 0.39875335
[61,] 0.773767029 0.39950601
[62,] 0.663837101 0.48943550
[63,] 0.290495456 0.81931351
[64,] 0.375527823 0.83195782
[65,] 0.509233990 0.88205528
[66,] 0.393813529 0.66249525
[67,] 0.343913220 0.90628888
[68,] 0.114261626 0.38117578
[69,] 0.438174555 0.39857855
[70,] 0.998319979 0.76235664
[71,] 0.148744727 0.79073302
[72,] 0.091795498 0.88557863
[73,] 0.101680394 0.72613086
[74,] 0.690507546 0.54408572
[75,] 0.449600598 1.05067984
[76,] 0.516213678 1.02469699
[77,] 0.125343029 0.69571809
[78,] 0.947639492 1.30001849
[79,] 0.915747165 0.57431267
[80,] 0.783665570 0.76740719
[81,] 0.538493875 1.04425794
[82,] 0.960010407 1.19164026
[83,] 0.238837483 0.90452036
[84,] 0.902082467 0.69491144
[85,] 0.931721891 0.60982120
[86,] 0.915621312 0.86457405
[87,] 0.553135887 0.41633223
[88,] 0.936564083 0.79245182
[89,] 0.300149242 0.86095837
[90,] 0.112359841 0.72940994
[91,] 0.854982856 1.13377885
[92,] 0.934447358 0.82621655
[93,] 0.284877481 0.96594381
[94,] 0.818572542 0.50611866
[95,] 0.329789969 1.02664211
[96,] 0.959627554 0.75207721
[97,] 0.896311414 1.23805094
[98,] 0.782896576 1.22388287
[99,] 0.476517900 1.03988453
[100,] 0.974156637 1.14627006
$delta
[,1]
[1,] 1
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 0
[8,] 0
[9,] 0
[10,] 0
[11,] 1
[12,] 0
[13,] 0
[14,] 0
[15,] 0
[16,] 0
[17,] 0
[18,] 0
[19,] 0
[20,] 0
[21,] 1
[22,] 1
[23,] 0
[24,] 0
[25,] 0
[26,] 0
[27,] 0
[28,] 0
[29,] 1
[30,] 0
[31,] 0
[32,] 0
[33,] 1
[34,] 0
[35,] 1
[36,] 1
[37,] 1
[38,] 0
[39,] 0
[40,] 1
[41,] 0
[42,] 0
[43,] 0
[44,] 1
[45,] 0
[46,] 0
[47,] 0
[48,] 0
[49,] 1
[50,] 1
[51,] 0
[52,] 0
[53,] 1
[54,] 0
[55,] 0
[56,] 0
[57,] 1
[58,] 0
[59,] 0
[60,] 0
[61,] 1
[62,] 0
[63,] 1
[64,] 0
[65,] 1
[66,] 1
[67,] 0
[68,] 1
[69,] 1
[70,] 0
[71,] 1
[72,] 1
[73,] 0
[74,] 1
[75,] 0
[76,] 0
[77,] 1
[78,] 0
[79,] 1
[80,] 1
[81,] 0
[82,] 0
[83,] 1
[84,] 0
[85,] 0
[86,] 0
[87,] 0
[88,] 0
[89,] 0
[90,] 1
[91,] 0
[92,] 0
[93,] 1
[94,] 0
[95,] 0
[96,] 0
[97,] 0
[98,] 0
[99,] 0
[100,] 0
$Pper
[1] 70
imputeYn documentation built on May 1, 2019, 10:52 p.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) References Examples
Description
This gives the survival data generated from log-normal AFT model.
Usage
1 | data(n, p, r, b1, sig, Cper)
|
Arguments
n |
sample size. |
p |
the number of covariates. For the AFT model each covariate is generated from Uniform(0, 1) distribution |
r |
correlation between the covariates, r is set to 0 for no correlation. |
b1 |
the vector of coefficients. |
sig |
this maintains noise ratio, 1 for no noise. |
Cper |
takes specific value for generating specific censoring percentage, e.g., -0.2 for 30 censoring percentage, 0.0 for 50 censoring percentage and 0.2 for 70 percentages. |
Details
Generate survival data from a log-normal AFT model (Y = alpha + X (beta) + error; Y=log(T)) where error is N(0,1). The last largest datum is generated always as censored otherwise censorship is random with censoring time generated from Uniform (c, 2c) for a suitable c.
Value
y |
logarithmic of survival time |
x |
matrix of covariates of order n by p |
delta |
status; 1 for uncensored, o for censored |
Pper |
censoring percentage |
Author(s)
Hasinur Rahaman Khan and Ewart Shaw
References
Khan and Shaw. (2013a). On Dealing with Censored Largest Observations under Weighted Least Squares. CRiSM working paper, Department of Statistics, University of Warwick, UK, No. 13-07. Also available in http://arxiv.org/abs/1312.2533.
Examples
1 2 3 4 5 6 7 8 9 | #Dataset with zero correlation between the covariates and the medium censoring level
#(50 percent)
data1<-data(n=100, p=2, r=0, b1=c(2,4), sig=1, Cper=0)
data1
#Dataset with moderate correlation between the covariates and the higher censoring level
#(70 percent)
data.r<-data(n=100, p=2, r=0.5, b1=c(2,4), sig=1, Cper=0.2)
data.r
|
Example output
Loading required package: quadprog
Loading required package: emplik
Loading required package: mvtnorm
Loading required package: survival
Loading required package: boot
Attaching package: ‘boot’
The following object is masked from ‘package:survival’:
aml
Attaching package: ‘imputeYn’
The following object is masked from ‘package:utils’:
data
$y
[,1]
[1,] -1.490596e+00
[2,] -1.448699e+00
[3,] -1.304946e+00
[4,] -1.140452e+00
[5,] -1.024939e+00
[6,] -1.016997e+00
[7,] -9.061287e-01
[8,] -8.775528e-01
[9,] -5.402613e-01
[10,] -4.510826e-01
[11,] -4.492635e-01
[12,] -3.202873e-01
[13,] -1.695147e-01
[14,] -1.368129e-01
[15,] -3.446866e-02
[16,] -7.969948e-05
[17,] 2.551893e-02
[18,] 1.327122e-01
[19,] 1.872044e-01
[20,] 2.215430e-01
[21,] 2.749025e-01
[22,] 2.842287e-01
[23,] 3.656798e-01
[24,] 3.926379e-01
[25,] 5.144067e-01
[26,] 5.843210e-01
[27,] 6.252607e-01
[28,] 6.978630e-01
[29,] 7.115890e-01
[30,] 7.275057e-01
[31,] 7.654093e-01
[32,] 9.580971e-01
[33,] 9.648227e-01
[34,] 1.032831e+00
[35,] 1.040238e+00
[36,] 1.109877e+00
[37,] 1.154714e+00
[38,] 1.187994e+00
[39,] 1.212367e+00
[40,] 1.314550e+00
[41,] 1.339962e+00
[42,] 1.362065e+00
[43,] 1.410882e+00
[44,] 1.490646e+00
[45,] 1.513951e+00
[46,] 1.580968e+00
[47,] 1.859841e+00
[48,] 1.887315e+00
[49,] 1.904084e+00
[50,] 1.985168e+00
[51,] 2.051422e+00
[52,] 2.094406e+00
[53,] 2.097436e+00
[54,] 2.133348e+00
[55,] 2.137555e+00
[56,] 2.159415e+00
[57,] 2.166578e+00
[58,] 2.197953e+00
[59,] 2.205251e+00
[60,] 2.213610e+00
[61,] 2.268682e+00
[62,] 2.358280e+00
[63,] 2.401979e+00
[64,] 2.425581e+00
[65,] 2.489497e+00
[66,] 2.518313e+00
[67,] 2.594513e+00
[68,] 2.609954e+00
[69,] 2.621219e+00
[70,] 2.629718e+00
[71,] 2.686806e+00
[72,] 2.887496e+00
[73,] 2.892745e+00
[74,] 2.922870e+00
[75,] 2.950506e+00
[76,] 3.092064e+00
[77,] 3.141766e+00
[78,] 3.193537e+00
[79,] 3.209344e+00
[80,] 3.297576e+00
[81,] 3.420199e+00
[82,] 3.439402e+00
[83,] 3.441932e+00
[84,] 3.444023e+00
[85,] 3.697358e+00
[86,] 3.898381e+00
[87,] 4.070555e+00
[88,] 4.112334e+00
[89,] 4.137917e+00
[90,] 4.193426e+00
[91,] 4.406721e+00
[92,] 4.440835e+00
[93,] 4.499303e+00
[94,] 4.718543e+00
[95,] 4.914510e+00
[96,] 5.036963e+00
[97,] 5.207800e+00
[98,] 5.476322e+00
[99,] 5.517171e+00
[100,] 6.483557e+00
$x
[,1] [,2]
[1,] 0.008285618 0.02004632
[2,] 0.603948027 0.04136400
[3,] 0.749886048 0.80537665
[4,] 0.268061888 0.64785515
[5,] 0.579744524 0.85515809
[6,] 0.670466864 0.88070744
[7,] 0.039840392 0.01954896
[8,] 0.305548955 0.72960546
[9,] 0.359227001 0.89164752
[10,] 0.689658555 0.54660851
[11,] 0.754070207 0.85070181
[12,] 0.800294591 0.54280922
[13,] 0.074289950 0.26769015
[14,] 0.239568133 0.97094194
[15,] 0.622065050 0.06828453
[16,] 0.727132641 0.27365789
[17,] 0.546636574 0.80279058
[18,] 0.802719830 0.31456396
[19,] 0.609042065 0.15779918
[20,] 0.819738729 0.27085236
[21,] 0.680980340 0.71784881
[22,] 0.868506235 0.66708590
[23,] 0.735999623 0.04362489
[24,] 0.140612081 0.17409860
[25,] 0.577776826 0.52482366
[26,] 0.986593809 0.13743821
[27,] 0.217697633 0.58492996
[28,] 0.238560191 0.18250626
[29,] 0.580880128 0.74624072
[30,] 0.382228391 0.77651939
[31,] 0.954001454 0.08329257
[32,] 0.229965508 0.85957270
[33,] 0.693629754 0.85071214
[34,] 0.373688609 0.16757145
[35,] 0.546343721 0.40440447
[36,] 0.265669918 0.23879413
[37,] 0.642581882 0.20311241
[38,] 0.732441386 0.58364495
[39,] 0.741724879 0.84501602
[40,] 0.281390808 0.87511534
[41,] 0.163431903 0.04918670
[42,] 0.104867396 0.13198850
[43,] 0.744740272 0.81764503
[44,] 0.131073454 0.90196323
[45,] 0.365897471 0.48585119
[46,] 0.184721524 0.62539224
[47,] 0.048235682 0.33119733
[48,] 0.123359561 0.02005913
[49,] 0.950732729 0.16068665
[50,] 0.368947438 0.46759172
[51,] 0.288823119 0.91767980
[52,] 0.381344867 0.19854325
[53,] 0.788756985 0.71178541
[54,] 0.392592578 0.26727408
[55,] 0.450617155 0.56031002
[56,] 0.110833225 0.76217824
[57,] 0.775727746 0.36956189
[58,] 0.401736462 0.33824809
[59,] 0.798350696 0.68388506
[60,] 0.849601799 0.86007808
[61,] 0.029630458 0.84507010
[62,] 0.114465718 0.51968629
[63,] 0.530401196 0.10902959
[64,] 0.456595083 0.77547613
[65,] 0.085689292 0.32625308
[66,] 0.975080423 0.39024683
[67,] 0.241971032 0.74734415
[68,] 0.696059793 0.84045058
[69,] 0.541718748 0.11816538
[70,] 0.396946717 0.17927819
[71,] 0.301907460 0.64145860
[72,] 0.238763664 0.82567239
[73,] 0.155480494 0.85043632
[74,] 0.468320030 0.20160606
[75,] 0.365256759 0.51141369
[76,] 0.793021146 0.36135729
[77,] 0.887595445 0.82627047
[78,] 0.942793358 0.71578495
[79,] 0.829833405 0.28091666
[80,] 0.610367620 0.60225763
[81,] 0.574682808 0.70943990
[82,] 0.238297680 0.90659999
[83,] 0.991291813 0.14671926
[84,] 0.007570231 0.76349598
[85,] 0.953918792 0.61001960
[86,] 0.730642145 0.70180084
[87,] 0.360288379 0.24620897
[88,] 0.134702833 0.69867497
[89,] 0.229572109 0.96540188
[90,] 0.562822985 0.79569573
[91,] 0.458305422 0.57656953
[92,] 0.191316289 0.82916908
[93,] 0.935334133 0.65727461
[94,] 0.302043875 0.95929916
[95,] 0.682437687 0.83224093
[96,] 0.370492648 0.96043441
[97,] 0.988907159 0.55368815
[98,] 0.833822708 0.87356512
[99,] 0.617153703 0.69374266
[100,] 0.662917295 0.95184023
$delta
[,1]
[1,] 1
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 1
[8,] 0
[9,] 0
[10,] 0
[11,] 0
[12,] 0
[13,] 0
[14,] 0
[15,] 1
[16,] 0
[17,] 0
[18,] 0
[19,] 1
[20,] 0
[21,] 0
[22,] 0
[23,] 0
[24,] 1
[25,] 0
[26,] 1
[27,] 1
[28,] 1
[29,] 0
[30,] 0
[31,] 0
[32,] 0
[33,] 0
[34,] 1
[35,] 1
[36,] 0
[37,] 0
[38,] 0
[39,] 0
[40,] 0
[41,] 1
[42,] 1
[43,] 0
[44,] 0
[45,] 0
[46,] 1
[47,] 1
[48,] 1
[49,] 1
[50,] 1
[51,] 0
[52,] 1
[53,] 0
[54,] 1
[55,] 1
[56,] 0
[57,] 0
[58,] 1
[59,] 0
[60,] 0
[61,] 1
[62,] 1
[63,] 1
[64,] 0
[65,] 1
[66,] 1
[67,] 0
[68,] 1
[69,] 1
[70,] 1
[71,] 1
[72,] 0
[73,] 0
[74,] 0
[75,] 0
[76,] 1
[77,] 1
[78,] 0
[79,] 1
[80,] 1
[81,] 1
[82,] 1
[83,] 1
[84,] 1
[85,] 1
[86,] 1
[87,] 1
[88,] 0
[89,] 0
[90,] 1
[91,] 1
[92,] 1
[93,] 1
[94,] 1
[95,] 1
[96,] 0
[97,] 1
[98,] 1
[99,] 1
[100,] 0
$Pper
[1] 50
$y
[,1]
[1,] -2.00081900
[2,] -1.98977696
[3,] -1.91927836
[4,] -1.82132514
[5,] -1.81987482
[6,] -1.73135488
[7,] -1.70653544
[8,] -1.62619379
[9,] -1.53584099
[10,] -1.39643230
[11,] -1.35130805
[12,] -1.30206533
[13,] -1.10592834
[14,] -0.74818002
[15,] -0.71102154
[16,] -0.59785034
[17,] -0.53070726
[18,] -0.51914616
[19,] -0.50289238
[20,] -0.44960559
[21,] -0.37325844
[22,] -0.31597869
[23,] -0.23623907
[24,] -0.07280976
[25,] -0.02442669
[26,] 0.03201953
[27,] 0.11599098
[28,] 0.12120679
[29,] 0.26608613
[30,] 0.31738677
[31,] 0.45064416
[32,] 0.52609660
[33,] 0.60190508
[34,] 0.61166043
[35,] 0.62186342
[36,] 0.63834095
[37,] 0.68220696
[38,] 0.86093913
[39,] 0.96055285
[40,] 1.03521196
[41,] 1.05558807
[42,] 1.24675233
[43,] 1.25380151
[44,] 1.43329805
[45,] 1.47717516
[46,] 1.48523742
[47,] 1.53953695
[48,] 1.56063522
[49,] 1.60393899
[50,] 1.65433458
[51,] 1.75532586
[52,] 1.83577334
[53,] 1.95271068
[54,] 2.05814127
[55,] 2.16348011
[56,] 2.29160458
[57,] 2.32457594
[58,] 2.34099761
[59,] 2.34982427
[60,] 2.45528632
[61,] 2.46239813
[62,] 2.51206258
[63,] 2.51480409
[64,] 2.60656767
[65,] 2.62068979
[66,] 2.68083623
[67,] 2.69643942
[68,] 2.70609530
[69,] 2.80432824
[70,] 2.90916822
[71,] 2.95498018
[72,] 2.95759585
[73,] 3.11129235
[74,] 3.11361063
[75,] 3.13801746
[76,] 3.37782138
[77,] 3.44313182
[78,] 3.54419455
[79,] 3.74833287
[80,] 3.74891717
[81,] 3.76361732
[82,] 3.80347343
[83,] 3.80911363
[84,] 3.82294230
[85,] 3.99019448
[86,] 4.01551187
[87,] 4.01983148
[88,] 4.16078641
[89,] 4.22717421
[90,] 4.40605029
[91,] 4.51652742
[92,] 4.52271285
[93,] 4.67712870
[94,] 4.70094896
[95,] 4.84780957
[96,] 4.85870941
[97,] 5.68137551
[98,] 5.83957891
[99,] 6.01000953
[100,] 6.01821177
$x
[,1] [,2]
[1,] 0.104132310 0.39267084
[2,] 0.732147299 1.18388207
[3,] 0.494005437 0.78034102
[4,] 0.990595904 0.82871002
[5,] 0.719762678 1.19623833
[6,] 0.158678906 0.92518932
[7,] 0.566521263 1.11380322
[8,] 0.831944648 0.91772891
[9,] 0.884370878 0.84801319
[10,] 0.275581250 0.47080631
[11,] 0.003151742 0.03846625
[12,] 0.912079474 0.55724741
[13,] 0.213539267 0.14151800
[14,] 0.383799729 0.27736820
[15,] 0.063233601 0.48986771
[16,] 0.603731662 0.52202852
[17,] 0.307617045 0.95416328
[18,] 0.929436242 0.83831423
[19,] 0.275955417 0.84540988
[20,] 0.156036330 0.19330358
[21,] 0.091499316 0.13796514
[22,] 0.150722792 0.16498462
[23,] 0.861986283 1.06960639
[24,] 0.239624630 0.96234059
[25,] 0.675493272 0.74051085
[26,] 0.357627908 0.76020211
[27,] 0.481756836 0.64825763
[28,] 0.383551049 0.82472182
[29,] 0.135659873 0.48920981
[30,] 0.484105288 0.48590694
[31,] 0.959735574 0.57941609
[32,] 0.414090431 1.03918724
[33,] 0.087663108 0.51947066
[34,] 0.615063014 0.69619659
[35,] 0.259916195 0.32924257
[36,] 0.148873104 0.76089358
[37,] 0.284802383 0.64342799
[38,] 0.775593658 1.13242453
[39,] 0.785706502 0.57509340
[40,] 0.397226878 0.32797422
[41,] 0.505933467 0.32774330
[42,] 0.224558837 0.89003381
[43,] 0.593637761 1.07230537
[44,] 0.291767699 0.26578603
[45,] 0.097319045 0.80863128
[46,] 0.960398150 0.98899906
[47,] 0.739743918 0.41327425
[48,] 0.577929757 0.62203579
[49,] 0.020161122 0.38388413
[50,] 0.272938660 0.21225485
[51,] 0.320465329 0.19205163
[52,] 0.577300053 0.47703343
[53,] 0.096317067 0.20605126
[54,] 0.506448317 1.09418243
[55,] 0.136715003 0.27729313
[56,] 0.757482575 0.70590554
[57,] 0.537896304 0.43256712
[58,] 0.631669580 1.04709937
[59,] 0.623746094 0.66542269
[60,] 0.779742509 0.39875335
[61,] 0.773767029 0.39950601
[62,] 0.663837101 0.48943550
[63,] 0.290495456 0.81931351
[64,] 0.375527823 0.83195782
[65,] 0.509233990 0.88205528
[66,] 0.393813529 0.66249525
[67,] 0.343913220 0.90628888
[68,] 0.114261626 0.38117578
[69,] 0.438174555 0.39857855
[70,] 0.998319979 0.76235664
[71,] 0.148744727 0.79073302
[72,] 0.091795498 0.88557863
[73,] 0.101680394 0.72613086
[74,] 0.690507546 0.54408572
[75,] 0.449600598 1.05067984
[76,] 0.516213678 1.02469699
[77,] 0.125343029 0.69571809
[78,] 0.947639492 1.30001849
[79,] 0.915747165 0.57431267
[80,] 0.783665570 0.76740719
[81,] 0.538493875 1.04425794
[82,] 0.960010407 1.19164026
[83,] 0.238837483 0.90452036
[84,] 0.902082467 0.69491144
[85,] 0.931721891 0.60982120
[86,] 0.915621312 0.86457405
[87,] 0.553135887 0.41633223
[88,] 0.936564083 0.79245182
[89,] 0.300149242 0.86095837
[90,] 0.112359841 0.72940994
[91,] 0.854982856 1.13377885
[92,] 0.934447358 0.82621655
[93,] 0.284877481 0.96594381
[94,] 0.818572542 0.50611866
[95,] 0.329789969 1.02664211
[96,] 0.959627554 0.75207721
[97,] 0.896311414 1.23805094
[98,] 0.782896576 1.22388287
[99,] 0.476517900 1.03988453
[100,] 0.974156637 1.14627006
$delta
[,1]
[1,] 1
[2,] 0
[3,] 0
[4,] 0
[5,] 0
[6,] 0
[7,] 0
[8,] 0
[9,] 0
[10,] 0
[11,] 1
[12,] 0
[13,] 0
[14,] 0
[15,] 0
[16,] 0
[17,] 0
[18,] 0
[19,] 0
[20,] 0
[21,] 1
[22,] 1
[23,] 0
[24,] 0
[25,] 0
[26,] 0
[27,] 0
[28,] 0
[29,] 1
[30,] 0
[31,] 0
[32,] 0
[33,] 1
[34,] 0
[35,] 1
[36,] 1
[37,] 1
[38,] 0
[39,] 0
[40,] 1
[41,] 0
[42,] 0
[43,] 0
[44,] 1
[45,] 0
[46,] 0
[47,] 0
[48,] 0
[49,] 1
[50,] 1
[51,] 0
[52,] 0
[53,] 1
[54,] 0
[55,] 0
[56,] 0
[57,] 1
[58,] 0
[59,] 0
[60,] 0
[61,] 1
[62,] 0
[63,] 1
[64,] 0
[65,] 1
[66,] 1
[67,] 0
[68,] 1
[69,] 1
[70,] 0
[71,] 1
[72,] 1
[73,] 0
[74,] 1
[75,] 0
[76,] 0
[77,] 1
[78,] 0
[79,] 1
[80,] 1
[81,] 0
[82,] 0
[83,] 1
[84,] 0
[85,] 0
[86,] 0
[87,] 0
[88,] 0
[89,] 0
[90,] 1
[91,] 0
[92,] 0
[93,] 1
[94,] 0
[95,] 0
[96,] 0
[97,] 0
[98,] 0
[99,] 0
[100,] 0
$Pper
[1] 70
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