Description Usage Arguments Value Author(s) Examples
The proportion explained by each eigenvalue and confidence intervals for each eigenvalue are computed via nonparametric bootstrap. When doing PCA, a natural question that arises when choosing the amount of components is whether the chosen set of eigenvalues conform a well defined set. If two eigenvalues are statistically equal, then the space spanned by them is not correctly defined, so consequently none of them should be included in the set of chosen eigenvalues. Ideally, the chosen set should include only eigenvalues that are statistically different between them, and also different respect to the other eigenvalues. On the other hand, it is usually important to compute a confidence interval for the proportion explained by the chosen set which is also addressed in this function.
1 | boot_pr_comp(valores, size, alpha, plot = TRUE)
|
valores |
A matrix with the dataset should be specified.This dataset should have the observations as rows and the variables as columns. |
size |
The amount of boostrap replicates. |
alpha |
The alpha, which is by default 0,05. |
plot |
A boolean value indicating whether the plot of the eigenvalues CIs should be produced. |
proportions_quantiles |
The upper and lower quantile for the explained proportion. Note that for k variables, only k-1 proportions are needed since k eigenvalues always explains the total variance |
proportions_used |
The boostrapped proportions used for the computation. It can be used to produce histograms |
eigen_quantiles |
The upper and lower quantile for the eigenvalues |
eigen_used |
The used eigenvalues for the eigenvalues |
Francisco Juretig
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | boot_pr_comp(as.matrix(iris[,1:4]))
function(valores,size=1000,alpha=0.05,plot=TRUE){
if (is.matrix(valores)==FALSE){
return ("Oject is not a matrix")
}else{
lengs = length(valores[,1])
hlengs = length(valores[1,])
store_bootstrap = matrix(0,size,hlengs)
elements_aux = NULL
indexes = seq(1,lengs,1)
work_matrix = matrix(0,lengs,hlengs)
empirical_quantiles1= matrix(0,hlengs-1,2)
store_eigen = matrix(0,size,hlengs)
empirical_quantiles2= matrix(0,hlengs,2)
for (sim in 1:size){
resample_indexes= sample(indexes,length(indexes), replace=T)
for (ips in 1:length(resample_indexes)){
work_matrix[ips,] = valores[resample_indexes[ips],]
}
cova = (lengs-1)*cov(work_matrix)/(lengs)
auto_va = unlist(eigen(cova)$values)
cum_eigen = cumsum(auto_va)
total_var = sum(auto_va)
percent = (cum_eigen/total_var)
store_bootstrap[sim,] = percent
store_eigen[sim,] = auto_va
}
store_bootstrap = store_bootstrap[,-hlengs]
for (iter in 1:(hlengs-1)){
empirical_quantiles1[iter,2] = quantile(store_bootstrap[,iter],1-alpha/2)
empirical_quantiles1[iter,1] = quantile(store_bootstrap[,iter],alpha/2)
}
for (iter in 1:(hlengs)){
empirical_quantiles2[iter,2] = quantile(store_eigen[,iter],1-alpha/2)
empirical_quantiles2[iter,1] = quantile(store_eigen[,iter],alpha/2)
}
if (plot==TRUE){
plot(0:max( empirical_quantiles2[,2]),0:max( empirical_quantiles2[,2]),
xlim=c(0,max( empirical_quantiles2)),ylim=c(0,nrow( empirical_quantiles2)),
type="n",xlab="Values",ylab="Eigenvalues")
for (q in 1:nrow(empirical_quantiles2)){
segments( empirical_quantiles2[q,1],q, empirical_quantiles2[q,2],q,lwd=2)
abline(v= empirical_quantiles2[q,1],lty = 3)
}
}
colnames(empirical_quantiles1) = c(paste(alpha/2*100,"%"),
paste((1-alpha/2)*100,"%"))
colnames(empirical_quantiles2) = c(paste(alpha/2*100,"%"),
paste((1-alpha/2)*100,"%"))
lista = list("proportions_quantiles" = empirical_quantiles1,
"proportions_used" = store_bootstrap,
"eigen_quantiles"= empirical_quantiles2,"eigen_used"=store_eigen)
return(lista)
}
}
|
$proportions_quantiles
2.5 % 97.5 %
[1,] 0.9083078 0.9383528
[2,] 0.9723327 0.9826521
[3,] 0.9931681 0.9963351
$proportions_used
[,1] [,2] [,3]
[1,] 0.9215936 0.9725221 0.9933997
[2,] 0.9237067 0.9781605 0.9958286
[3,] 0.9363677 0.9796772 0.9952248
[4,] 0.9318408 0.9785907 0.9948977
[5,] 0.9283152 0.9782674 0.9962053
[6,] 0.9285544 0.9763430 0.9940601
[7,] 0.9173178 0.9733782 0.9940065
[8,] 0.9186419 0.9796296 0.9953409
[9,] 0.9228076 0.9773456 0.9950044
[10,] 0.9274159 0.9762168 0.9954941
[11,] 0.9133982 0.9721645 0.9941713
[12,] 0.9261818 0.9830938 0.9960672
[13,] 0.9283694 0.9804640 0.9950547
[14,] 0.9254052 0.9773487 0.9957123
[15,] 0.9292127 0.9817383 0.9950005
[16,] 0.9181727 0.9771468 0.9956652
[17,] 0.9273074 0.9826490 0.9953977
[18,] 0.9326426 0.9784970 0.9960010
[19,] 0.9291142 0.9814283 0.9954570
[20,] 0.9339807 0.9763369 0.9947395
[21,] 0.9215452 0.9792076 0.9949113
[22,] 0.9371671 0.9805552 0.9953198
[23,] 0.9276382 0.9791163 0.9941589
[24,] 0.9352371 0.9784765 0.9953017
[25,] 0.9337106 0.9810797 0.9959584
[26,] 0.9150830 0.9728523 0.9939543
[27,] 0.9299915 0.9799410 0.9956171
[28,] 0.9265507 0.9770434 0.9944977
[29,] 0.9174276 0.9764371 0.9932040
[30,] 0.9302251 0.9809786 0.9939008
[31,] 0.9289621 0.9790270 0.9946771
[32,] 0.9394592 0.9813081 0.9952334
[33,] 0.9316479 0.9743650 0.9945082
[34,] 0.9247639 0.9781051 0.9950821
[35,] 0.9096137 0.9753658 0.9950545
[36,] 0.9276011 0.9786044 0.9944957
[37,] 0.9251996 0.9810937 0.9955657
[38,] 0.9236140 0.9800212 0.9951059
[39,] 0.9241019 0.9782615 0.9953919
[40,] 0.9318722 0.9785701 0.9950154
[41,] 0.9211314 0.9816743 0.9950084
[42,] 0.9264564 0.9759629 0.9953453
[43,] 0.9247263 0.9790869 0.9954510
[44,] 0.9389301 0.9833366 0.9961660
[45,] 0.9459343 0.9838443 0.9951498
[46,] 0.9225332 0.9783895 0.9940907
[47,] 0.9324387 0.9805423 0.9945940
[48,] 0.9265799 0.9789452 0.9937611
[49,] 0.9237737 0.9821632 0.9953022
[50,] 0.9136941 0.9740769 0.9942077
[51,] 0.9239504 0.9799580 0.9954663
[52,] 0.9224643 0.9783044 0.9937731
[53,] 0.9249791 0.9815761 0.9949139
[54,] 0.9276840 0.9760867 0.9939049
[55,] 0.9191269 0.9762557 0.9940802
[56,] 0.9186783 0.9789542 0.9949963
[57,] 0.9263165 0.9754104 0.9945717
[58,] 0.9201095 0.9776593 0.9941384
[59,] 0.9331211 0.9818473 0.9959987
[60,] 0.9338275 0.9796381 0.9956144
[61,] 0.9363712 0.9821007 0.9952129
[62,] 0.9168660 0.9807480 0.9948080
[63,] 0.9322591 0.9792734 0.9951441
[64,] 0.9217332 0.9795169 0.9951085
[65,] 0.9327245 0.9775076 0.9951336
[66,] 0.9235006 0.9765512 0.9943334
[67,] 0.9177409 0.9782462 0.9950466
[68,] 0.9308980 0.9806635 0.9938574
[69,] 0.9263351 0.9790568 0.9963455
[70,] 0.9284301 0.9802555 0.9962544
[71,] 0.9354072 0.9766929 0.9941084
[72,] 0.9283305 0.9736862 0.9950429
[73,] 0.9204434 0.9793005 0.9955181
[74,] 0.9260689 0.9732625 0.9928511
[75,] 0.9297671 0.9788035 0.9944649
[76,] 0.9340690 0.9778519 0.9960909
[77,] 0.9210552 0.9794100 0.9956967
[78,] 0.9280877 0.9773282 0.9950268
[79,] 0.9162935 0.9774523 0.9939953
[80,] 0.9156167 0.9775904 0.9945347
[81,] 0.9235528 0.9774583 0.9941419
[82,] 0.9408092 0.9805066 0.9953324
[83,] 0.9340481 0.9806135 0.9940724
[84,] 0.9186575 0.9739844 0.9949813
[85,] 0.9274819 0.9769682 0.9941924
[86,] 0.9318580 0.9780646 0.9954229
[87,] 0.9217233 0.9792849 0.9959296
[88,] 0.9156163 0.9772415 0.9943309
[89,] 0.9180432 0.9805535 0.9943702
[90,] 0.9258194 0.9775676 0.9944011
[91,] 0.9240406 0.9785334 0.9941064
[92,] 0.9293238 0.9799344 0.9955234
[93,] 0.9267767 0.9819092 0.9961225
[94,] 0.9268908 0.9811490 0.9956730
[95,] 0.9186815 0.9789227 0.9937615
[96,] 0.9298665 0.9775899 0.9945509
[97,] 0.9166103 0.9733730 0.9927506
[98,] 0.9245670 0.9773107 0.9949811
[99,] 0.9254964 0.9832126 0.9952328
[100,] 0.9269799 0.9771512 0.9948487
[101,] 0.9350906 0.9801150 0.9962719
[102,] 0.9332412 0.9784995 0.9945267
[103,] 0.9184286 0.9760263 0.9952723
[104,] 0.9268043 0.9768654 0.9957914
[105,] 0.9383478 0.9830610 0.9950360
[106,] 0.9047408 0.9716905 0.9928113
[107,] 0.9206166 0.9742794 0.9941336
[108,] 0.9321411 0.9816485 0.9956612
[109,] 0.9295302 0.9751920 0.9940013
[110,] 0.9186198 0.9796376 0.9950596
[111,] 0.9056301 0.9711703 0.9950367
[112,] 0.9194265 0.9802294 0.9948779
[113,] 0.9314188 0.9814618 0.9943887
[114,] 0.9277716 0.9763698 0.9953969
[115,] 0.9261825 0.9793016 0.9941411
[116,] 0.9255803 0.9774387 0.9938321
[117,] 0.9147196 0.9782477 0.9951467
[118,] 0.9218630 0.9759998 0.9949280
[119,] 0.9292267 0.9816314 0.9948744
[120,] 0.9260899 0.9789763 0.9957659
[121,] 0.9293613 0.9799354 0.9952444
[122,] 0.9159828 0.9688112 0.9948136
[123,] 0.9260102 0.9757532 0.9947447
[124,] 0.9193469 0.9788215 0.9937441
[125,] 0.9333037 0.9809669 0.9947750
[126,] 0.9163874 0.9769961 0.9951208
[127,] 0.9255079 0.9790156 0.9952664
[128,] 0.9260744 0.9783546 0.9950369
[129,] 0.9190083 0.9781080 0.9962087
[130,] 0.9216204 0.9758152 0.9952037
[131,] 0.9265880 0.9752330 0.9936721
[132,] 0.9229992 0.9792844 0.9947409
[133,] 0.9186771 0.9805473 0.9961175
[134,] 0.9251788 0.9786010 0.9952651
[135,] 0.9300001 0.9770501 0.9937674
[136,] 0.9277385 0.9825462 0.9948869
[137,] 0.9174265 0.9750337 0.9942672
[138,] 0.9341387 0.9785296 0.9942122
[139,] 0.9257301 0.9808799 0.9951621
[140,] 0.9237824 0.9774200 0.9942743
[141,] 0.9281985 0.9791231 0.9951634
[142,] 0.9276764 0.9811959 0.9957834
[143,] 0.9319716 0.9779098 0.9947718
[144,] 0.9248545 0.9850411 0.9965502
[145,] 0.9349930 0.9829236 0.9959814
[146,] 0.9208561 0.9780261 0.9950859
[147,] 0.9337374 0.9776274 0.9951756
[148,] 0.9200826 0.9766921 0.9964063
[149,] 0.9254122 0.9786063 0.9957273
[150,] 0.9100244 0.9753865 0.9946436
[151,] 0.9303462 0.9728389 0.9949430
[152,] 0.9219570 0.9761657 0.9949641
[153,] 0.9287874 0.9763897 0.9953032
[154,] 0.9224787 0.9804294 0.9943442
[155,] 0.9325488 0.9855059 0.9962128
[156,] 0.9354961 0.9813271 0.9948602
[157,] 0.9328587 0.9768571 0.9946925
[158,] 0.9320529 0.9831057 0.9955935
[159,] 0.9278058 0.9759305 0.9945889
[160,] 0.9252912 0.9749328 0.9949543
[161,] 0.9231712 0.9816026 0.9947356
[162,] 0.9344255 0.9813413 0.9940977
[163,] 0.9299518 0.9776193 0.9955400
[164,] 0.9260039 0.9812477 0.9958168
[165,] 0.9239946 0.9790907 0.9943925
[166,] 0.9192395 0.9757472 0.9941542
[167,] 0.9141298 0.9768803 0.9956577
[168,] 0.9052578 0.9759082 0.9966853
[169,] 0.9319721 0.9797980 0.9947024
[170,] 0.9325302 0.9795377 0.9946103
[171,] 0.9325745 0.9786473 0.9943907
[172,] 0.9239120 0.9761800 0.9952295
[173,] 0.9327936 0.9805871 0.9961278
[174,] 0.9224875 0.9779524 0.9951265
[175,] 0.9188093 0.9794238 0.9963614
[176,] 0.9171322 0.9759364 0.9953343
[177,] 0.9278223 0.9759555 0.9949469
[178,] 0.9369393 0.9813255 0.9963132
[179,] 0.9182878 0.9764175 0.9950174
[180,] 0.9231167 0.9756577 0.9949831
[181,] 0.9227484 0.9799009 0.9959648
[182,] 0.9182805 0.9772330 0.9939324
[183,] 0.9264919 0.9774920 0.9947268
[184,] 0.9263454 0.9769871 0.9953023
[185,] 0.9234254 0.9761749 0.9945993
[186,] 0.9305998 0.9791665 0.9959868
[187,] 0.9287022 0.9757768 0.9943727
[188,] 0.9302296 0.9814566 0.9940287
[189,] 0.9265165 0.9807055 0.9954170
[190,] 0.9212980 0.9789500 0.9951403
[191,] 0.9266098 0.9754041 0.9952207
[192,] 0.9088831 0.9728154 0.9939210
[193,] 0.9367362 0.9830815 0.9949377
[194,] 0.9251168 0.9742882 0.9953939
[195,] 0.9160979 0.9760737 0.9938173
[196,] 0.9227888 0.9786482 0.9940885
[197,] 0.9260291 0.9769663 0.9952850
[198,] 0.9283809 0.9775791 0.9953947
[199,] 0.9177323 0.9776765 0.9947084
[200,] 0.9163928 0.9802012 0.9949654
[201,] 0.9270686 0.9784874 0.9940059
[202,] 0.9233699 0.9795972 0.9943985
[203,] 0.9182928 0.9718397 0.9939330
[204,] 0.9335898 0.9781597 0.9958063
[205,] 0.9014482 0.9825130 0.9958630
[206,] 0.9273607 0.9769486 0.9933698
[207,] 0.9098689 0.9766982 0.9953206
[208,] 0.9231685 0.9786039 0.9959693
[209,] 0.9228757 0.9771618 0.9942295
[210,] 0.9343610 0.9762919 0.9946515
[211,] 0.9362157 0.9791328 0.9958645
[212,] 0.9100075 0.9687488 0.9940574
[213,] 0.9361099 0.9817895 0.9940068
[214,] 0.9190148 0.9799545 0.9943930
[215,] 0.9204076 0.9732976 0.9949898
[216,] 0.9354423 0.9799140 0.9953654
[217,] 0.9282859 0.9791247 0.9946160
[218,] 0.9220593 0.9787142 0.9931687
[219,] 0.9173398 0.9781234 0.9949539
[220,] 0.9318359 0.9770398 0.9939757
[221,] 0.9459894 0.9829464 0.9966084
[222,] 0.9335678 0.9796749 0.9957776
[223,] 0.9153784 0.9812341 0.9960710
[224,] 0.9200097 0.9775060 0.9944151
[225,] 0.9291174 0.9744653 0.9927873
[226,] 0.9358007 0.9779137 0.9958021
[227,] 0.9272449 0.9779898 0.9941514
[228,] 0.9273677 0.9795200 0.9949987
[229,] 0.9198674 0.9724753 0.9945713
[230,] 0.9236116 0.9768888 0.9950768
[231,] 0.9222967 0.9774459 0.9949588
[232,] 0.9190472 0.9769564 0.9946793
[233,] 0.9181474 0.9815662 0.9960806
[234,] 0.9290179 0.9828811 0.9956021
[235,] 0.9215082 0.9773503 0.9940065
[236,] 0.9098742 0.9777132 0.9955664
[237,] 0.9302037 0.9804884 0.9957326
[238,] 0.9305051 0.9807159 0.9955667
[239,] 0.9245169 0.9745716 0.9947813
[240,] 0.9386246 0.9763471 0.9947884
[241,] 0.9285107 0.9783688 0.9956338
[242,] 0.9106843 0.9751796 0.9936599
[243,] 0.9253956 0.9786420 0.9961206
[244,] 0.9286632 0.9806307 0.9946174
[245,] 0.9268797 0.9798151 0.9967169
[246,] 0.9392338 0.9780566 0.9946311
[247,] 0.9279484 0.9762318 0.9963627
[248,] 0.9192520 0.9772745 0.9946042
[249,] 0.9311826 0.9782091 0.9956429
[250,] 0.9268728 0.9744624 0.9948243
[251,] 0.9280244 0.9750491 0.9932523
[252,] 0.9264000 0.9791773 0.9948617
[253,] 0.9259116 0.9780954 0.9935630
[254,] 0.9023792 0.9690053 0.9949903
[255,] 0.9299743 0.9777868 0.9947390
[256,] 0.9261723 0.9786567 0.9948128
[257,] 0.9292465 0.9791240 0.9960020
[258,] 0.9324390 0.9780869 0.9956330
[259,] 0.9275917 0.9800992 0.9949210
[260,] 0.9197677 0.9773158 0.9938319
[261,] 0.9306826 0.9803369 0.9959076
[262,] 0.9242601 0.9762426 0.9942136
[263,] 0.9271513 0.9769372 0.9950521
[264,] 0.9197973 0.9800529 0.9964859
[265,] 0.9231072 0.9773996 0.9938925
[266,] 0.9317950 0.9797832 0.9955112
[267,] 0.9300604 0.9816550 0.9946388
[268,] 0.9130427 0.9791332 0.9955790
[269,] 0.9157323 0.9689071 0.9924665
[270,] 0.9252361 0.9768022 0.9939756
[271,] 0.9122613 0.9751049 0.9942454
[272,] 0.9420363 0.9842226 0.9958428
[273,] 0.9192215 0.9769707 0.9951372
[274,] 0.9241678 0.9768441 0.9935809
[275,] 0.9363264 0.9792892 0.9958247
[276,] 0.9256483 0.9775762 0.9940861
[277,] 0.9225858 0.9779930 0.9944978
[278,] 0.9310745 0.9787771 0.9953412
[279,] 0.9217194 0.9786337 0.9951502
[280,] 0.9226798 0.9739784 0.9938773
[281,] 0.9146752 0.9736774 0.9946684
[282,] 0.9278815 0.9790253 0.9953274
[283,] 0.9343617 0.9776825 0.9945815
[284,] 0.9300841 0.9763705 0.9948208
[285,] 0.9369288 0.9790879 0.9953315
[286,] 0.9142092 0.9777287 0.9961784
[287,] 0.9142108 0.9747459 0.9952269
[288,] 0.9184249 0.9810397 0.9956338
[289,] 0.9147492 0.9752907 0.9944658
[290,] 0.9185991 0.9741624 0.9951504
[291,] 0.9288601 0.9799632 0.9941309
[292,] 0.9201110 0.9775793 0.9943755
[293,] 0.9247449 0.9824766 0.9951879
[294,] 0.9194683 0.9768094 0.9937785
[295,] 0.9263122 0.9803329 0.9943319
[296,] 0.9331469 0.9764392 0.9941982
[297,] 0.9239779 0.9780062 0.9946409
[298,] 0.9356726 0.9801100 0.9957427
[299,] 0.9339145 0.9799522 0.9949177
[300,] 0.9207244 0.9749684 0.9935782
[301,] 0.9288915 0.9776864 0.9947166
[302,] 0.9234813 0.9750234 0.9954095
[303,] 0.9218472 0.9795531 0.9966713
[304,] 0.9218464 0.9736346 0.9941539
[305,] 0.9170509 0.9783725 0.9957683
[306,] 0.9339369 0.9799860 0.9940999
[307,] 0.9375388 0.9817208 0.9950898
[308,] 0.9094122 0.9729218 0.9942666
[309,] 0.9219849 0.9776352 0.9958005
[310,] 0.9217251 0.9741333 0.9941095
[311,] 0.9235299 0.9821518 0.9959146
[312,] 0.9260586 0.9797645 0.9964716
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[688,] 0.9263017 0.9743111 0.9951576
[689,] 0.9211781 0.9804953 0.9944122
[690,] 0.9269893 0.9783638 0.9945421
[691,] 0.9104307 0.9725119 0.9945755
[692,] 0.9286024 0.9792577 0.9950346
[693,] 0.9257849 0.9772260 0.9955080
[694,] 0.9364333 0.9803325 0.9948754
[695,] 0.9327743 0.9779775 0.9958602
[696,] 0.9106332 0.9792858 0.9960288
[697,] 0.9178447 0.9743026 0.9942032
[698,] 0.9341757 0.9786582 0.9964457
[699,] 0.9273553 0.9819619 0.9956085
[700,] 0.9168925 0.9770620 0.9955939
[701,] 0.9165447 0.9759949 0.9950320
[702,] 0.9316887 0.9764988 0.9953288
[703,] 0.9289114 0.9792766 0.9944989
[704,] 0.9273459 0.9806662 0.9964427
[705,] 0.9261068 0.9808017 0.9949419
[706,] 0.9245330 0.9778337 0.9948429
[707,] 0.9205155 0.9771169 0.9933281
[708,] 0.9136947 0.9752233 0.9944223
[709,] 0.9276657 0.9787076 0.9948439
[710,] 0.9228565 0.9727207 0.9944468
[711,] 0.9256337 0.9753788 0.9942186
[712,] 0.9235211 0.9781075 0.9964336
[713,] 0.9311543 0.9781508 0.9938618
[714,] 0.9246337 0.9813388 0.9942186
[715,] 0.9233772 0.9754109 0.9945103
[716,] 0.9130579 0.9766165 0.9946548
[717,] 0.9144608 0.9754102 0.9951126
[718,] 0.9154017 0.9758222 0.9947161
[719,] 0.9305260 0.9836106 0.9964160
[720,] 0.9336118 0.9766625 0.9934651
[721,] 0.9230023 0.9774356 0.9941999
[722,] 0.9120445 0.9752504 0.9947686
[723,] 0.9252146 0.9778411 0.9947762
[724,] 0.9320805 0.9782497 0.9941329
[725,] 0.9246497 0.9749252 0.9948198
[726,] 0.9122360 0.9750937 0.9938513
[727,] 0.9223946 0.9758133 0.9946138
[728,] 0.9223818 0.9757089 0.9940961
[729,] 0.9263858 0.9782908 0.9937283
[730,] 0.9241847 0.9732317 0.9933522
[731,] 0.9152233 0.9777750 0.9947112
[732,] 0.9207253 0.9761817 0.9955366
[733,] 0.9220078 0.9800114 0.9940899
[734,] 0.9307536 0.9727751 0.9945989
[735,] 0.9385469 0.9812412 0.9957605
[736,] 0.9254379 0.9754925 0.9939919
[737,] 0.9449075 0.9815772 0.9951655
[738,] 0.9278402 0.9754147 0.9940286
[739,] 0.9303797 0.9766393 0.9961076
[740,] 0.9318372 0.9774540 0.9950781
[741,] 0.9262849 0.9798947 0.9954967
[742,] 0.9290433 0.9786330 0.9952393
[743,] 0.9286474 0.9771696 0.9958441
[744,] 0.9165352 0.9766370 0.9948997
[745,] 0.9205223 0.9790419 0.9944659
[746,] 0.9165469 0.9775060 0.9956773
[747,] 0.9192032 0.9762007 0.9948741
[748,] 0.9288569 0.9748238 0.9955736
[749,] 0.9197657 0.9736641 0.9942331
[750,] 0.9323070 0.9781091 0.9948678
[751,] 0.9171650 0.9746888 0.9946464
[752,] 0.9260044 0.9796595 0.9954102
[753,] 0.9283446 0.9772055 0.9953839
[754,] 0.9292158 0.9779380 0.9944413
[755,] 0.9260647 0.9778667 0.9953203
[756,] 0.9249820 0.9808946 0.9954204
[757,] 0.9033754 0.9775636 0.9929372
[758,] 0.9319053 0.9756321 0.9951115
[759,] 0.9188007 0.9813716 0.9954273
[760,] 0.9181429 0.9719133 0.9931822
[761,] 0.9216541 0.9764042 0.9952359
[762,] 0.9238668 0.9793794 0.9955347
[763,] 0.9303667 0.9791629 0.9955494
[764,] 0.9378500 0.9814811 0.9955384
[765,] 0.9214266 0.9799904 0.9960896
[766,] 0.9263533 0.9796364 0.9950111
[767,] 0.9276856 0.9797606 0.9957026
[768,] 0.9055838 0.9746629 0.9941053
[769,] 0.9227959 0.9757949 0.9948353
[770,] 0.9276566 0.9738396 0.9958666
[771,] 0.9366070 0.9780150 0.9933155
[772,] 0.9218551 0.9790109 0.9954825
[773,] 0.9191019 0.9741770 0.9949011
[774,] 0.9184512 0.9805150 0.9952688
[775,] 0.9173473 0.9828045 0.9954860
[776,] 0.9175586 0.9767618 0.9955280
[777,] 0.9142537 0.9780281 0.9947747
[778,] 0.9203706 0.9798874 0.9950172
[779,] 0.9231961 0.9799081 0.9946286
[780,] 0.9157563 0.9774162 0.9938066
[781,] 0.9301694 0.9813308 0.9962081
[782,] 0.9374275 0.9784145 0.9939454
[783,] 0.9151683 0.9785811 0.9953208
[784,] 0.9141365 0.9711325 0.9928229
[785,] 0.9099946 0.9776434 0.9955465
[786,] 0.9312110 0.9795122 0.9958009
[787,] 0.9174055 0.9763556 0.9937487
[788,] 0.9188546 0.9775357 0.9939026
[789,] 0.9286823 0.9779615 0.9955361
[790,] 0.9275269 0.9797913 0.9956506
[791,] 0.9281195 0.9732412 0.9932413
[792,] 0.9213455 0.9750619 0.9944268
[793,] 0.9293646 0.9760838 0.9951544
[794,] 0.9194800 0.9794056 0.9947939
[795,] 0.9278301 0.9764971 0.9945656
[796,] 0.9194834 0.9770356 0.9952377
[797,] 0.9273981 0.9809764 0.9951529
[798,] 0.9171793 0.9757373 0.9932430
[799,] 0.9303812 0.9805490 0.9966095
[800,] 0.9099436 0.9765602 0.9948806
[801,] 0.9258139 0.9793821 0.9952119
[802,] 0.9363032 0.9779813 0.9944499
[803,] 0.9278824 0.9796445 0.9942439
[804,] 0.9341161 0.9764554 0.9953056
[805,] 0.9345336 0.9806664 0.9958818
[806,] 0.9148715 0.9770731 0.9938024
[807,] 0.9114670 0.9757165 0.9937025
[808,] 0.9251058 0.9802235 0.9955804
[809,] 0.9068066 0.9779185 0.9950628
[810,] 0.9402699 0.9817559 0.9951107
[811,] 0.9169173 0.9760539 0.9956473
[812,] 0.9237549 0.9758917 0.9954480
[813,] 0.9278769 0.9794457 0.9949683
[814,] 0.9241577 0.9729210 0.9951624
[815,] 0.9354078 0.9792191 0.9963348
[816,] 0.9213529 0.9759545 0.9948762
[817,] 0.9181799 0.9803105 0.9938903
[818,] 0.9131811 0.9710686 0.9924104
[819,] 0.9343061 0.9843861 0.9953888
[820,] 0.9184873 0.9835137 0.9942709
[821,] 0.9233299 0.9740012 0.9935641
[822,] 0.9375262 0.9800330 0.9949917
[823,] 0.9239245 0.9789699 0.9941716
[824,] 0.9246783 0.9763099 0.9931338
[825,] 0.9197845 0.9769701 0.9946289
[826,] 0.9243104 0.9752184 0.9952225
[827,] 0.9361875 0.9810494 0.9947398
[828,] 0.9182860 0.9791210 0.9955021
[829,] 0.9245324 0.9798126 0.9952871
[830,] 0.9141704 0.9709489 0.9942395
[831,] 0.9112234 0.9713891 0.9951490
[832,] 0.9139241 0.9714996 0.9947817
[833,] 0.9055334 0.9718347 0.9928178
[834,] 0.9364448 0.9789792 0.9940704
[835,] 0.9159265 0.9796598 0.9949076
[836,] 0.9256014 0.9765225 0.9940025
[837,] 0.9190341 0.9772159 0.9946582
[838,] 0.9100037 0.9740686 0.9928295
[839,] 0.9358228 0.9822824 0.9961413
[840,] 0.9015340 0.9724765 0.9924903
[841,] 0.9182964 0.9737027 0.9923372
[842,] 0.9218973 0.9763639 0.9943793
[843,] 0.9336199 0.9794674 0.9956074
[844,] 0.9178651 0.9811637 0.9954317
[845,] 0.9236200 0.9766673 0.9937843
[846,] 0.9153051 0.9776743 0.9946257
[847,] 0.9347115 0.9803971 0.9958395
[848,] 0.9283530 0.9794970 0.9946738
[849,] 0.9366510 0.9773896 0.9949215
[850,] 0.9179765 0.9726789 0.9951098
[851,] 0.9273219 0.9797011 0.9957389
[852,] 0.9253115 0.9786061 0.9942074
[853,] 0.9351426 0.9816215 0.9949764
[854,] 0.9224209 0.9760652 0.9942299
[855,] 0.9272080 0.9726320 0.9938256
[856,] 0.9286726 0.9819686 0.9955866
[857,] 0.9290352 0.9773624 0.9956371
[858,] 0.9090152 0.9741906 0.9947274
[859,] 0.9203492 0.9778382 0.9947290
[860,] 0.9307044 0.9797175 0.9955313
[861,] 0.9313991 0.9798010 0.9955825
[862,] 0.9234654 0.9825763 0.9958790
[863,] 0.9327962 0.9813718 0.9961641
[864,] 0.9404008 0.9803799 0.9961620
[865,] 0.9288817 0.9797359 0.9935542
[866,] 0.9266586 0.9801382 0.9953196
[867,] 0.9224196 0.9795331 0.9950083
[868,] 0.9314544 0.9786038 0.9942057
[869,] 0.9237157 0.9765978 0.9948863
[870,] 0.9304886 0.9818500 0.9954318
[871,] 0.9218368 0.9793503 0.9943727
[872,] 0.9134756 0.9810578 0.9961642
[873,] 0.9292442 0.9734523 0.9947742
[874,] 0.9388160 0.9777406 0.9931439
[875,] 0.9385784 0.9819755 0.9948658
[876,] 0.9244875 0.9770347 0.9935591
[877,] 0.9364967 0.9793369 0.9954319
[878,] 0.9329568 0.9798294 0.9953114
[879,] 0.9100355 0.9784706 0.9940724
[880,] 0.9188419 0.9753002 0.9949633
[881,] 0.9343350 0.9784296 0.9942429
[882,] 0.9325813 0.9774131 0.9956349
[883,] 0.9295796 0.9792014 0.9955363
[884,] 0.9344807 0.9755667 0.9943232
[885,] 0.9222574 0.9784477 0.9951762
[886,] 0.9301259 0.9759562 0.9951501
[887,] 0.9255533 0.9804709 0.9947469
[888,] 0.9280456 0.9821630 0.9952498
[889,] 0.9381563 0.9797891 0.9956153
[890,] 0.9206589 0.9796485 0.9941258
[891,] 0.9169349 0.9761976 0.9945962
[892,] 0.9180580 0.9784116 0.9946057
[893,] 0.9283039 0.9791680 0.9952372
[894,] 0.9247094 0.9772460 0.9954227
[895,] 0.9223762 0.9810607 0.9959110
[896,] 0.9213203 0.9745868 0.9943251
[897,] 0.9271951 0.9791948 0.9949492
[898,] 0.9256259 0.9742539 0.9955797
[899,] 0.9220405 0.9755439 0.9958330
[900,] 0.9297531 0.9807702 0.9945273
[901,] 0.9205318 0.9745753 0.9941173
[902,] 0.9328480 0.9784574 0.9958401
[903,] 0.9227917 0.9760506 0.9949385
[904,] 0.9147283 0.9757831 0.9958563
[905,] 0.9104554 0.9735733 0.9947922
[906,] 0.9240237 0.9793343 0.9952492
[907,] 0.9344064 0.9792544 0.9963500
[908,] 0.9252197 0.9737469 0.9945273
[909,] 0.9354083 0.9761810 0.9940611
[910,] 0.9304477 0.9796704 0.9953861
[911,] 0.9146526 0.9775712 0.9952189
[912,] 0.9315626 0.9738338 0.9933336
[913,] 0.9214984 0.9734686 0.9949932
[914,] 0.9366225 0.9823733 0.9946039
[915,] 0.9362454 0.9781654 0.9952739
[916,] 0.9292932 0.9743475 0.9942088
[917,] 0.9216233 0.9761033 0.9944404
[918,] 0.9280516 0.9779959 0.9946100
[919,] 0.9247055 0.9753586 0.9946077
[920,] 0.9370009 0.9790555 0.9958656
[921,] 0.9191108 0.9819954 0.9955812
[922,] 0.9359253 0.9759776 0.9956258
[923,] 0.9301181 0.9780528 0.9950642
[924,] 0.9093256 0.9699284 0.9933534
[925,] 0.9229975 0.9812554 0.9957680
[926,] 0.9161416 0.9792875 0.9945019
[927,] 0.9309593 0.9773117 0.9933895
[928,] 0.9150096 0.9812539 0.9958849
[929,] 0.9288611 0.9765116 0.9938973
[930,] 0.9199567 0.9780348 0.9948132
[931,] 0.9251630 0.9791889 0.9956903
[932,] 0.9112702 0.9762200 0.9949273
[933,] 0.9301348 0.9770903 0.9939602
[934,] 0.9311300 0.9817367 0.9952620
[935,] 0.9228058 0.9799578 0.9961180
[936,] 0.9298554 0.9781651 0.9942128
[937,] 0.9236923 0.9802424 0.9955993
[938,] 0.9296984 0.9766271 0.9948385
[939,] 0.9253046 0.9785988 0.9952592
[940,] 0.9200933 0.9823978 0.9947177
[941,] 0.9132869 0.9764151 0.9943725
[942,] 0.9362986 0.9823422 0.9953472
[943,] 0.9219265 0.9803517 0.9954803
[944,] 0.9256528 0.9800784 0.9942111
[945,] 0.9358741 0.9813044 0.9957687
[946,] 0.9131786 0.9748704 0.9940403
[947,] 0.9149681 0.9778669 0.9949631
[948,] 0.9193912 0.9762874 0.9957170
[949,] 0.9387380 0.9799366 0.9943283
[950,] 0.9352172 0.9799815 0.9955838
[951,] 0.9266074 0.9792968 0.9962267
[952,] 0.9321202 0.9797474 0.9951455
[953,] 0.9324886 0.9757276 0.9945709
[954,] 0.9229457 0.9833672 0.9952457
[955,] 0.9294339 0.9763743 0.9949136
[956,] 0.9254964 0.9784564 0.9948942
[957,] 0.9183795 0.9818050 0.9948361
[958,] 0.9211979 0.9750787 0.9948420
[959,] 0.9205162 0.9793003 0.9947054
[960,] 0.9236946 0.9800312 0.9955507
[961,] 0.9238015 0.9774186 0.9944742
[962,] 0.9278614 0.9784305 0.9948682
[963,] 0.9256279 0.9793104 0.9955302
[964,] 0.9269468 0.9747009 0.9937722
[965,] 0.9319718 0.9784181 0.9940883
[966,] 0.9229306 0.9800074 0.9962292
[967,] 0.9239756 0.9781732 0.9944818
[968,] 0.9120900 0.9728255 0.9937193
[969,] 0.9294066 0.9771137 0.9935433
[970,] 0.9221625 0.9806830 0.9955096
[971,] 0.9026066 0.9742508 0.9922875
[972,] 0.9302212 0.9813386 0.9954690
[973,] 0.9364559 0.9797281 0.9958561
[974,] 0.9297623 0.9772062 0.9943919
[975,] 0.9305863 0.9778654 0.9952995
[976,] 0.9357661 0.9777372 0.9950007
[977,] 0.9309466 0.9783849 0.9940928
[978,] 0.9100606 0.9789887 0.9952612
[979,] 0.9268950 0.9812717 0.9960160
[980,] 0.9251374 0.9771424 0.9937096
[981,] 0.9244903 0.9761115 0.9947938
[982,] 0.9192818 0.9801523 0.9953325
[983,] 0.9351016 0.9794826 0.9958025
[984,] 0.9244688 0.9805465 0.9949029
[985,] 0.9280909 0.9793938 0.9939273
[986,] 0.9326900 0.9748480 0.9941812
[987,] 0.9288755 0.9758863 0.9943870
[988,] 0.9257148 0.9754758 0.9951444
[989,] 0.9301101 0.9772230 0.9934291
[990,] 0.9309045 0.9810184 0.9959628
[991,] 0.9108774 0.9786484 0.9937845
[992,] 0.9218116 0.9769884 0.9949162
[993,] 0.9258126 0.9801541 0.9954443
[994,] 0.9271305 0.9801144 0.9952318
[995,] 0.9081526 0.9759854 0.9948548
[996,] 0.9235967 0.9785597 0.9957822
[997,] 0.9243217 0.9732614 0.9941965
[998,] 0.9344517 0.9799745 0.9956550
[999,] 0.9280058 0.9786595 0.9947993
[1000,] 0.9109437 0.9782425 0.9943734
$eigen_quantiles
2.5 % 97.5 %
[1,] 3.62695705 4.72675151
[2,] 0.18451818 0.29638727
[3,] 0.05884472 0.09430172
[4,] 0.01710371 0.03001819
$eigen_used
[,1] [,2] [,3] [,4]
[1,] 4.014121 0.2218257 0.09093496 0.02874845
[2,] 4.155585 0.2449775 0.07948571 0.01876630
[3,] 4.804333 0.2222130 0.07977203 0.02450071
[4,] 4.177331 0.2095746 0.07310203 0.02287316
[5,] 4.236471 0.2279627 0.08186134 0.01731773
[6,] 3.892996 0.2003554 0.07427942 0.02490336
[7,] 3.829744 0.2340487 0.08612179 0.02502236
[8,] 3.927267 0.2607272 0.06716709 0.01991784
[9,] 4.418752 0.2611489 0.08455670 0.02392102
[10,] 4.111983 0.2163741 0.08547165 0.01997831
[11,] 3.658886 0.2354057 0.08815504 0.02334845
[12,] 4.599900 0.2826549 0.06443227 0.01953247
[13,] 4.164754 0.2337013 0.06545532 0.02218513
[14,] 4.212606 0.2364560 0.08359444 0.01951815
[15,] 4.776854 0.2700214 0.06817757 0.02570114
[16,] 3.995068 0.2566026 0.08057567 0.01886121
[17,] 4.093209 0.2442821 0.05627385 0.02031475
[18,] 4.552927 0.2238500 0.08544983 0.01952226
[19,] 4.419830 0.2488597 0.06673511 0.02161127
[20,] 4.461426 0.2023265 0.08790491 0.02512847
[21,] 3.944597 0.2468193 0.06721852 0.02178155
[22,] 4.295602 0.1988734 0.06767503 0.02145241
[23,] 3.993713 0.2216257 0.06476242 0.02514720
[24,] 4.553267 0.2105141 0.08191460 0.02287407
[25,] 4.371849 0.2217932 0.06966548 0.01892363
[26,] 3.947968 0.2492356 0.09104103 0.02608303
[27,] 4.530425 0.2433276 0.07636565 0.02135124
[28,] 3.998774 0.2179145 0.07532868 0.02374665
[29,] 4.093676 0.2633078 0.07481622 0.03032439
[30,] 4.619575 0.2520463 0.06417291 0.03028890
[31,] 4.806643 0.2590466 0.08097687 0.02754157
[32,] 4.261309 0.1898230 0.06316388 0.02162104
[33,] 4.086304 0.1873613 0.08835046 0.02408747
[34,] 3.750650 0.2163406 0.06885532 0.01994602
[35,] 3.618009 0.2615304 0.07831235 0.01967089
[36,] 4.129754 0.2270706 0.07074924 0.02450566
[37,] 4.016144 0.2426274 0.06282083 0.01924860
[38,] 4.313508 0.2634358 0.07044906 0.02285678
[39,] 4.004943 0.2347211 0.07424090 0.01997113
[40,] 4.567529 0.2288876 0.08060579 0.02443186
[41,] 3.962458 0.2604391 0.05735960 0.02147254
[42,] 4.542669 0.2427438 0.09503717 0.02282323
[43,] 4.349550 0.2556912 0.07697016 0.02139674
[44,] 4.212963 0.1992513 0.05756512 0.01720322
[45,] 4.298738 0.1722793 0.05137721 0.02204148
[46,] 4.208752 0.2548257 0.07163126 0.02695934
[47,] 4.441224 0.2291181 0.06692869 0.02574883
[48,] 3.936841 0.2224891 0.06294972 0.02650777
[49,] 4.537286 0.2867908 0.06453486 0.02307402
[50,] 4.127674 0.2727832 0.09094229 0.02616724
[51,] 4.027512 0.2441377 0.06760082 0.01976257
[52,] 4.170918 0.2524807 0.06994197 0.02815477
[53,] 4.349901 0.2661589 0.06272360 0.02391858
[54,] 4.071679 0.2124433 0.07820554 0.02675176
[55,] 3.580024 0.2225183 0.06942678 0.02305791
[56,] 4.099540 0.2689776 0.07158657 0.02232870
[57,] 4.205174 0.2228705 0.08698566 0.02464293
[58,] 4.238404 0.2650979 0.07590947 0.02700114
[59,] 4.770428 0.2491045 0.07234669 0.02045621
[60,] 4.345316 0.2131674 0.07434165 0.02040701
[61,] 4.779716 0.2334267 0.06693138 0.02443588
[62,] 4.222054 0.2941685 0.06474497 0.02390831
[63,] 4.202462 0.2119326 0.07154224 0.02188959
[64,] 3.970651 0.2489215 0.06716540 0.02107171
[65,] 4.314780 0.2071662 0.08153776 0.02251199
[66,] 4.277362 0.2457133 0.08236185 0.02624574
[67,] 3.630858 0.2393773 0.06646719 0.01959728
[68,] 4.111803 0.2198157 0.05827801 0.02713196
[69,] 4.568995 0.2600412 0.08527368 0.01802531
[70,] 4.241781 0.2367781 0.07309519 0.01711278
[71,] 4.244636 0.1873439 0.07902680 0.02673468
[72,] 4.107935 0.2007024 0.09450506 0.02193544
[73,] 4.038582 0.2582443 0.07115700 0.01966500
[74,] 4.086422 0.2082490 0.08643762 0.03154566
[75,] 4.186488 0.2207975 0.07051908 0.02492315
[76,] 4.285081 0.2008557 0.08367256 0.01793295
[77,] 4.192585 0.2656276 0.07413614 0.01958817
[78,] 4.429039 0.2349866 0.08446171 0.02373316
[79,] 3.978666 0.2655594 0.07183169 0.02607337
[80,] 4.027092 0.2725745 0.07452506 0.02403766
[81,] 4.388727 0.2561593 0.07928024 0.02783782
[82,] 4.726746 0.1994449 0.07448654 0.02345085
[83,] 4.327285 0.2157293 0.06235280 0.02746174
[84,] 3.632992 0.2187999 0.08303587 0.01984723
[85,] 4.236660 0.2260495 0.07867869 0.02652846
[86,] 4.348020 0.2155982 0.08099336 0.02135664
[87,] 4.170116 0.2604236 0.07530475 0.01841573
[88,] 4.115268 0.2769767 0.07680871 0.02547993
[89,] 4.121341 0.2806255 0.06202699 0.02527359
[90,] 3.931310 0.2197387 0.07147998 0.02377460
[91,] 3.974402 0.2343797 0.06698152 0.02534885
[92,] 4.081093 0.2222550 0.06845831 0.01965887
[93,] 4.507112 0.2681211 0.06912224 0.01885714
[94,] 4.508385 0.2639113 0.07064478 0.02104639
[95,] 4.102617 0.2690232 0.06626674 0.02785963
[96,] 4.360108 0.2237732 0.07952924 0.02555065
[97,] 3.950020 0.2446121 0.08350546 0.03124037
[98,] 4.149260 0.2367028 0.07930108 0.02252365
[99,] 4.552064 0.2838778 0.05912130 0.02344770
[100,] 4.190634 0.2268113 0.08000586 0.02328750
[101,] 4.547646 0.2189685 0.07857617 0.01813076
[102,] 4.118875 0.1997483 0.07073646 0.02415645
[103,] 4.270871 0.2678403 0.08949743 0.02198489
[104,] 4.004584 0.2163067 0.08177633 0.01818469
[105,] 4.205025 0.2003736 0.05366369 0.02224526
[106,] 3.496319 0.2587233 0.08161994 0.02778046
[107,] 3.903709 0.2275474 0.08418814 0.02487550
[108,] 4.827080 0.2563732 0.07256442 0.02246859
[109,] 4.267242 0.2096220 0.08634901 0.02753839
[110,] 3.973014 0.2639009 0.06669963 0.02136725
[111,] 3.511070 0.2540949 0.09252854 0.01924248
[112,] 4.331521 0.2864490 0.06901056 0.02413098
[113,] 4.575744 0.2458445 0.06350523 0.02756656
[114,] 3.943847 0.2065851 0.08088201 0.01956728
[115,] 4.416164 0.2532790 0.07075686 0.02793611
[116,] 3.833719 0.2147959 0.06790084 0.02554701
[117,] 4.143355 0.2877595 0.07654683 0.02198353
[118,] 3.760388 0.2208303 0.07721027 0.02068924
[119,] 4.353979 0.2455472 0.06205161 0.02401626
[120,] 4.642335 0.2651108 0.08416349 0.02122504
[121,] 4.487672 0.2442106 0.07392359 0.02296385
[122,] 3.710517 0.2140004 0.10533219 0.02100921
[123,] 3.854542 0.2070565 0.07905268 0.02187532
[124,] 4.222327 0.2731519 0.06853543 0.02873193
[125,] 4.221057 0.2155668 0.06244983 0.02363117
[126,] 4.147275 0.2742953 0.08202666 0.02208176
[127,] 3.859021 0.2231069 0.06775982 0.01973720
[128,] 4.049228 0.2285933 0.07294287 0.02170104
[129,] 3.701103 0.2380107 0.07289667 0.01526866
[130,] 4.198867 0.2469095 0.08833355 0.02185154
[131,] 4.015854 0.2108284 0.07991553 0.02742519
[132,] 3.969795 0.2420813 0.06647785 0.02261926
[133,] 4.443837 0.2992791 0.07531637 0.01878056
[134,] 4.244707 0.2451000 0.07645499 0.02172347
[135,] 4.098565 0.2073524 0.07367383 0.02746759
[136,] 4.441383 0.2623818 0.05907879 0.02447824
[137,] 4.006833 0.2515977 0.08400142 0.02503805
[138,] 4.345982 0.2065237 0.07296174 0.02692717
[139,] 4.257653 0.2536472 0.06568700 0.02225079
[140,] 4.188008 0.2431685 0.07640938 0.02595781
[141,] 4.331234 0.2376283 0.07484875 0.02256878
[142,] 4.461797 0.2574100 0.07016046 0.02028053
[143,] 4.207633 0.2074002 0.07612790 0.02360410
[144,] 4.287035 0.2789863 0.05334887 0.01599116
[145,] 4.310079 0.2209479 0.06019331 0.01852449
[146,] 4.413046 0.2739778 0.08175581 0.02355018
[147,] 4.158403 0.1954639 0.07815102 0.02148562
[148,] 3.796358 0.2335769 0.08134298 0.01482786
[149,] 3.700305 0.2126991 0.06845913 0.01708478
[150,] 3.583913 0.2574128 0.07583958 0.02109486
[151,] 4.111633 0.1877949 0.09768817 0.02234938
[152,] 3.928068 0.2309604 0.08009191 0.02145594
[153,] 4.025526 0.2063165 0.08197438 0.02035687
[154,] 4.141142 0.2601493 0.06246548 0.02538993
[155,] 4.665852 0.2649621 0.05357018 0.01894874
[156,] 4.446807 0.2178539 0.06432839 0.02443182
[157,] 4.330760 0.2042608 0.08280014 0.02463994
[158,] 4.392232 0.2405827 0.05884767 0.02076530
[159,] 4.260189 0.2209733 0.08567364 0.02484590
[160,] 3.838238 0.2059204 0.08305192 0.02093044
[161,] 4.229340 0.2676928 0.06016648 0.02411808
[162,] 4.446003 0.2232256 0.06069480 0.02808334
[163,] 4.081210 0.2091947 0.07864731 0.01957315
[164,] 4.141114 0.2470521 0.06515316 0.01870745
[165,] 4.301554 0.2564935 0.07123579 0.02610521
[166,] 3.985288 0.2449844 0.07980194 0.02534411
[167,] 4.049533 0.2779806 0.08318272 0.01923605
[168,] 3.953467 0.3085465 0.09073815 0.01447603
[169,] 4.458967 0.2288205 0.07130896 0.02534622
[170,] 3.869862 0.1950745 0.06254890 0.02236643
[171,] 4.389479 0.2168574 0.07410151 0.02640218
[172,] 4.052611 0.2292664 0.08355773 0.02092522
[173,] 4.595826 0.2354762 0.07656840 0.01907792
[174,] 4.092122 0.2460405 0.07618373 0.02161852
[175,] 4.444818 0.2932277 0.08193699 0.01760220
[176,] 3.967805 0.2544055 0.08392164 0.02018522
[177,] 4.439710 0.2303218 0.09087528 0.02417961
[178,] 4.959299 0.2349399 0.07933109 0.01951479
[179,] 3.814234 0.2414498 0.07725721 0.02069585
[180,] 3.879224 0.2207937 0.08121108 0.02108272
[181,] 3.877297 0.2401491 0.06749919 0.01695534
[182,] 3.756061 0.2411344 0.06830596 0.02481844
[183,] 4.123228 0.2269691 0.07670095 0.02346769
[184,] 4.251550 0.2324253 0.08405904 0.02156063
[185,] 4.160801 0.2376803 0.08301748 0.02433461
[186,] 4.459935 0.2327575 0.08061201 0.01923349
[187,] 4.293318 0.2176223 0.08596759 0.02601444
[188,] 4.679015 0.2576695 0.06323704 0.03003540
[189,] 4.263687 0.2493691 0.06770007 0.02109045
[190,] 4.417467 0.2764316 0.07762960 0.02330135
[191,] 4.225237 0.2224962 0.09036156 0.02179315
[192,] 3.704447 0.2605764 0.08602284 0.02477696
[193,] 4.719894 0.2335179 0.05973920 0.02550744
[194,] 3.937235 0.2092704 0.08982461 0.01960304
[195,] 3.627186 0.2374675 0.07025366 0.02447990
[196,] 4.127900 0.2498751 0.06906905 0.02644372
[197,] 4.183670 0.2301272 0.08276128 0.02130160
[198,] 4.143499 0.2195787 0.07951374 0.02055410
[199,] 4.019009 0.2625126 0.07458774 0.02317331
[200,] 3.790127 0.2639061 0.06106376 0.02082264
[201,] 4.373745 0.2425847 0.07321376 0.02827895
[202,] 4.006637 0.2439784 0.06422504 0.02430563
[203,] 3.413653 0.1990549 0.08212926 0.02255346
[204,] 4.049147 0.1933078 0.07653615 0.01818900
[205,] 4.064983 0.3655528 0.06020038 0.01865541
[206,] 4.020530 0.2149861 0.07119351 0.02874478
[207,] 4.183048 0.3072425 0.08561498 0.02151297
[208,] 4.383747 0.2632399 0.08246103 0.01914029
[209,] 3.889629 0.2287986 0.07193515 0.02432080
[210,] 3.991499 0.1791249 0.07843035 0.02284816
[211,] 4.532341 0.2077670 0.08100037 0.02002065
[212,] 3.919545 0.2530084 0.10900781 0.02559584
[213,] 4.258876 0.2078214 0.05558300 0.02726653
[214,] 3.723404 0.2468984 0.05849770 0.02271694
[215,] 3.881607 0.2230515 0.09148196 0.02112942
[216,] 4.808668 0.2286081 0.07942831 0.02382437
[217,] 4.353868 0.2384454 0.07265754 0.02525212
[218,] 4.082067 0.2508178 0.06399189 0.03024292
[219,] 4.045970 0.2680891 0.07423179 0.02225586
[220,] 4.279600 0.2076057 0.07778079 0.02766747
[221,] 4.723371 0.1845277 0.06821530 0.01693435
[222,] 4.219799 0.2084076 0.07278536 0.01908575
[223,] 4.211619 0.3029993 0.06826389 0.01807732
[224,] 4.160695 0.2600241 0.07647026 0.02525753
[225,] 3.830129 0.1869394 0.07552903 0.02973334
[226,] 4.355119 0.1959897 0.08325055 0.01953672
[227,] 4.172523 0.2283477 0.07272596 0.02631824
[228,] 4.155736 0.2337057 0.06936353 0.02241186
[229,] 3.878875 0.2218357 0.09317392 0.02289167
[230,] 3.609422 0.2082045 0.07107740 0.01923970
[231,] 4.404387 0.2633627 0.08363238 0.02407381
[232,] 3.835923 0.2417013 0.07397189 0.02220765
[233,] 3.879324 0.2679552 0.06132540 0.01656032
[234,] 4.736587 0.2746207 0.06485778 0.02242288
[235,] 4.019183 0.2435567 0.07264625 0.02614100
[236,] 4.172043 0.3110620 0.08186210 0.02032945
[237,] 4.080022 0.2205568 0.06686347 0.01871746
[238,] 4.356970 0.2351054 0.06953702 0.02075841
[239,] 3.977118 0.2153272 0.08693883 0.02244987
[240,] 4.223145 0.1697243 0.08297281 0.02344842
[241,] 4.497578 0.2415061 0.08362917 0.02114918
[242,] 4.008352 0.2838746 0.08134030 0.02790580
[243,] 4.104365 0.2361614 0.07752206 0.01720604
[244,] 3.899433 0.2182102 0.05872994 0.02260129
[245,] 4.008694 0.2289422 0.07309922 0.01419901
[246,] 4.300233 0.1777484 0.07588541 0.02458128
[247,] 4.221259 0.2196426 0.09157607 0.01654594
[248,] 4.124883 0.2603597 0.07776188 0.02421225
[249,] 4.039307 0.2039927 0.07562463 0.01890030
[250,] 3.876671 0.1990450 0.08516408 0.02164747
[251,] 4.108692 0.2081950 0.08059218 0.02987443
[252,] 4.689380 0.2671557 0.07939318 0.02600980
[253,] 4.240342 0.2389832 0.07083621 0.02947911
[254,] 3.411395 0.2518762 0.09823475 0.01893898
[255,] 3.811606 0.1959649 0.06948057 0.02156271
[256,] 4.519320 0.2561011 0.07883477 0.02531125
[257,] 4.021922 0.2158775 0.07305078 0.01730378
[258,] 4.453619 0.2180282 0.08380596 0.02085799
[259,] 4.057283 0.2296680 0.06483022 0.02221567
[260,] 3.931404 0.2459802 0.07059580 0.02636446
[261,] 4.177283 0.2228688 0.06988736 0.01836845
[262,] 3.891708 0.2188785 0.07566912 0.02436422
[263,] 3.972078 0.2132914 0.07760750 0.02119757
[264,] 4.250815 0.2784693 0.07594477 0.01624037
[265,] 4.034714 0.2373011 0.07208701 0.02669460
[266,] 4.144836 0.2134627 0.06996144 0.01996738
[267,] 4.050160 0.2246806 0.05654106 0.02334644
[268,] 4.027372 0.2915209 0.07254137 0.01950066
[269,] 3.720311 0.2160313 0.09571403 0.03060595
[270,] 3.983355 0.2220041 0.07393542 0.02593642
[271,] 3.850506 0.2652528 0.08078875 0.02428933
[272,] 4.860504 0.2176633 0.05995539 0.02144944
[273,] 3.875744 0.2434896 0.07659608 0.02050327
[274,] 4.105255 0.2339940 0.07434666 0.02851441
[275,] 4.591263 0.2106677 0.08108118 0.02047369
[276,] 4.310762 0.2418294 0.07688660 0.02754128
[277,] 4.249625 0.2552172 0.07602476 0.02534429
[278,] 4.595490 0.2354451 0.08175544 0.02299418
[279,] 4.051774 0.2501889 0.07260490 0.02131900
[280,] 3.933176 0.2186741 0.08482455 0.02609979
[281,] 4.377939 0.2824039 0.10047004 0.02551864
[282,] 4.633095 0.2553709 0.08139973 0.02333126
[283,] 4.489408 0.2081472 0.08119587 0.02603475
[284,] 4.370907 0.2175218 0.08670677 0.02433938
[285,] 4.484727 0.2018000 0.07775168 0.02234655
[286,] 3.885887 0.2699924 0.07842112 0.01624406
[287,] 4.195224 0.2777896 0.09398520 0.02190349
[288,] 4.184585 0.2852893 0.06649481 0.01989333
[289,] 3.948911 0.2613536 0.08277738 0.02389084
[290,] 3.888925 0.2352294 0.08885348 0.02053091
[291,] 4.265214 0.2346592 0.06505653 0.02695007
[292,] 4.018689 0.2509993 0.07335922 0.02456559
[293,] 4.281580 0.2672986 0.05885324 0.02228018
[294,] 4.132154 0.2576947 0.07626004 0.02796007
[295,] 4.067919 0.2372330 0.06147680 0.02489150
[296,] 3.946770 0.1831058 0.07511214 0.02453900
[297,] 3.985567 0.2330506 0.07175337 0.02311662
[298,] 4.492159 0.2133439 0.07505250 0.02043906
[299,] 4.089071 0.2015723 0.06552566 0.02225226
[300,] 4.263510 0.2511827 0.08617449 0.02973686
[301,] 4.325081 0.2271977 0.07929530 0.02460054
[302,] 4.098259 0.2287356 0.09046982 0.02037201
[303,] 4.168700 0.2609527 0.07741067 0.01505279
[304,] 4.111026 0.2309523 0.09150695 0.02607112
[305,] 4.250267 0.2842075 0.08062476 0.01961269
[306,] 4.079766 0.2011587 0.06165478 0.02577359
[307,] 4.726977 0.2227613 0.06740507 0.02475696
[308,] 3.462187 0.2417847 0.08126086 0.02182756
[309,] 4.155810 0.2508418 0.08187906 0.01892921
[310,] 3.995825 0.2271975 0.08660014 0.02553631
[311,] 4.502320 0.2857891 0.06709512 0.01991696
[312,] 4.657695 0.2701187 0.08403000 0.01774640
[313,] 4.106598 0.2791599 0.08287705 0.01777840
[314,] 4.416740 0.2178032 0.07332868 0.02245701
[315,] 4.461696 0.2551338 0.07528223 0.02220012
[316,] 4.474576 0.2116879 0.09134374 0.02306673
[317,] 3.972646 0.2191965 0.06802902 0.02322539
[318,] 3.833744 0.2216265 0.07353919 0.02550924
[319,] 4.313936 0.2158603 0.08602482 0.01693209
[320,] 4.177331 0.2466502 0.06683537 0.03119269
[321,] 4.051305 0.2625660 0.07525796 0.02050289
[322,] 3.806066 0.2220702 0.08244407 0.02465049
[323,] 3.838277 0.2237202 0.07856781 0.01889340
[324,] 4.782230 0.2189716 0.06787292 0.02996079
[325,] 4.124418 0.1796964 0.08136449 0.02053696
[326,] 4.305764 0.2396876 0.08140814 0.02302252
[327,] 3.765151 0.2932929 0.06226025 0.03001790
[328,] 4.262405 0.2618507 0.08142736 0.02528656
[329,] 4.155472 0.2259292 0.08809677 0.01995787
[330,] 4.152332 0.2835422 0.08014290 0.01731167
[331,] 4.255991 0.2833612 0.07070238 0.02319134
[332,] 4.200520 0.2230896 0.07778673 0.02571421
[333,] 4.158723 0.2642345 0.08209945 0.02830223
[334,] 4.011996 0.2252793 0.08181310 0.03026569
[335,] 4.305358 0.2202074 0.07539911 0.02258923
[336,] 3.976022 0.2540485 0.07581182 0.02209610
[337,] 4.548244 0.2475926 0.08089127 0.02364544
[338,] 3.653102 0.2890100 0.07774419 0.01982774
[339,] 4.696420 0.2231788 0.06847001 0.02109018
[340,] 4.084219 0.2057976 0.07288537 0.02112568
[341,] 4.454443 0.2483434 0.06482676 0.02868135
[342,] 4.244555 0.2295548 0.07012654 0.02619344
[343,] 4.377997 0.2622384 0.07188630 0.02239273
[344,] 4.648088 0.2369318 0.07778553 0.02162951
[345,] 4.323677 0.2460707 0.08319041 0.01977115
[346,] 4.186298 0.2301393 0.07769108 0.02895555
[347,] 4.405027 0.2021532 0.05863867 0.02635713
[348,] 4.112238 0.2023249 0.07465147 0.02255946
[349,] 3.916362 0.2558297 0.08358950 0.02545916
[350,] 4.276893 0.2117320 0.05564382 0.02434603
[351,] 4.230599 0.2513912 0.08483704 0.02626429
[352,] 4.300695 0.2526941 0.07040540 0.01922991
[353,] 3.962619 0.2538110 0.07445629 0.02147876
[354,] 4.402425 0.2319107 0.08221416 0.02386174
[355,] 4.265759 0.2162947 0.07439465 0.02479606
[356,] 4.014828 0.2141948 0.08145528 0.02758835
[357,] 3.464274 0.2466116 0.09141976 0.02048470
[358,] 4.631546 0.2259154 0.08344379 0.02428698
[359,] 4.429694 0.3266801 0.06738649 0.02210079
[360,] 4.075002 0.1943339 0.07642579 0.02602402
[361,] 3.670365 0.2270622 0.08195146 0.02187687
[362,] 4.358798 0.2155190 0.07585957 0.01938580
[363,] 4.411682 0.2405254 0.07354690 0.02264873
[364,] 4.001941 0.2132191 0.07857266 0.02798396
[365,] 4.525248 0.2733896 0.07799159 0.02340218
[366,] 4.232370 0.2339438 0.07810387 0.02366591
[367,] 4.088891 0.2512037 0.07563371 0.02511592
[368,] 3.965655 0.2288419 0.07101570 0.02363179
[369,] 4.612548 0.2792964 0.07335589 0.02717913
[370,] 4.575771 0.2079079 0.08225367 0.02456121
[371,] 4.680681 0.2527726 0.08723447 0.02558233
[372,] 4.138815 0.2138249 0.09031364 0.02287345
[373,] 4.780438 0.2986960 0.07557624 0.02404296
[374,] 4.179450 0.2503746 0.09642332 0.02108952
[375,] 4.627873 0.2684600 0.09126183 0.01817323
[376,] 3.743361 0.2865086 0.08623635 0.02574704
[377,] 4.068523 0.2869215 0.06405830 0.01850150
[378,] 4.340488 0.2196989 0.07552498 0.01767739
[379,] 4.028607 0.2261445 0.07498756 0.01974118
[380,] 4.552292 0.2461699 0.07985371 0.01702571
[381,] 3.707016 0.1909943 0.06832805 0.02461146
[382,] 3.720270 0.2198854 0.06925668 0.02077227
[383,] 3.939218 0.2054397 0.07610220 0.02437247
[384,] 4.164346 0.2365424 0.07131760 0.02741591
[385,] 4.210826 0.2125905 0.07646962 0.01828520
[386,] 4.157031 0.2477107 0.06998492 0.01921108
[387,] 4.071793 0.2266262 0.08511655 0.02153152
[388,] 4.240527 0.2600632 0.07031366 0.02182229
[389,] 4.475814 0.1841470 0.07798698 0.02866781
[390,] 4.044184 0.2125006 0.07145987 0.01651954
[391,] 4.193573 0.2024599 0.07748797 0.02388632
[392,] 4.166935 0.2754785 0.07765570 0.02403526
[393,] 4.401822 0.2166118 0.08216965 0.02584324
[394,] 4.121297 0.2518202 0.08206746 0.02687870
[395,] 4.194876 0.2922112 0.07930562 0.02508030
[396,] 4.012239 0.2349793 0.07079125 0.02447170
[397,] 4.342046 0.2631909 0.08811302 0.02303764
[398,] 4.515011 0.1877496 0.08244649 0.02480061
[399,] 4.224218 0.2147067 0.06594125 0.02324019
[400,] 3.895940 0.2739768 0.08198761 0.01701944
[401,] 4.023742 0.2038211 0.07014052 0.02186036
[402,] 4.184823 0.2219291 0.07494537 0.02228487
[403,] 4.502500 0.2005611 0.07657018 0.02234560
[404,] 4.145040 0.2693090 0.06400130 0.02663024
[405,] 4.403229 0.2419145 0.06420828 0.02425660
[406,] 4.291878 0.2040290 0.07617937 0.02554539
[407,] 4.530447 0.2101479 0.07643952 0.02689347
[408,] 4.203750 0.2164583 0.07275366 0.01584749
[409,] 4.452843 0.2714288 0.08217302 0.02678369
[410,] 4.108284 0.2162320 0.09166037 0.02234051
[411,] 4.272971 0.2522502 0.06921478 0.02277894
[412,] 4.261977 0.2547488 0.07211564 0.02288280
[413,] 3.880073 0.2095210 0.07732805 0.02028969
[414,] 3.459960 0.2633438 0.07880271 0.02769803
[415,] 4.252898 0.2057176 0.08465302 0.02100951
[416,] 4.214957 0.2627692 0.07742360 0.01599253
[417,] 4.142164 0.2713395 0.08129767 0.02022869
[418,] 3.595036 0.2322597 0.08262892 0.02370840
[419,] 4.310024 0.2315165 0.06495955 0.02495020
[420,] 3.757197 0.2153490 0.07801644 0.02020648
[421,] 3.756041 0.2224783 0.05834006 0.02409125
[422,] 4.447937 0.2607714 0.06455196 0.02123126
[423,] 4.551593 0.2339616 0.06178438 0.02165631
[424,] 4.677534 0.2684793 0.07707952 0.02369414
[425,] 4.426309 0.2477190 0.07761238 0.02120676
[426,] 4.531917 0.1949828 0.06650930 0.02636619
[427,] 4.299477 0.2551803 0.06854648 0.02289285
[428,] 3.809129 0.2158215 0.08013629 0.02213094
[429,] 4.482098 0.2526061 0.08376816 0.02124238
[430,] 3.428589 0.1957170 0.07810259 0.02371804
[431,] 4.066258 0.1767987 0.07830867 0.02204567
[432,] 3.991035 0.2683848 0.06225340 0.02702893
[433,] 4.280216 0.2247522 0.07958720 0.02297180
[434,] 4.044286 0.3073923 0.08045507 0.02102509
[435,] 4.204243 0.2657973 0.06981862 0.01880445
[436,] 4.084272 0.2867125 0.06489557 0.02127842
[437,] 3.688229 0.2492302 0.07197542 0.02355075
[438,] 4.113523 0.2634980 0.08300262 0.01805904
[439,] 4.245369 0.1901094 0.07327028 0.02444047
[440,] 4.683886 0.3064086 0.07847560 0.02233332
[441,] 3.508821 0.2488777 0.08419832 0.02195884
[442,] 4.272617 0.1937148 0.07189661 0.02757160
[443,] 4.147811 0.2276890 0.08122587 0.02212738
[444,] 4.593322 0.2524364 0.08727418 0.01969000
[445,] 4.436179 0.2496175 0.07621258 0.02558562
[446,] 4.377180 0.2052471 0.08251128 0.02925823
[447,] 3.798461 0.2502362 0.07471278 0.02396592
[448,] 4.218488 0.2386991 0.08229443 0.02283015
[449,] 4.111721 0.2343792 0.07898011 0.02301178
[450,] 3.996992 0.2562904 0.07055749 0.02175839
[451,] 3.519297 0.2509363 0.09673185 0.01980377
[452,] 3.900064 0.2044088 0.07202644 0.02126168
[453,] 4.241971 0.2298150 0.07338022 0.02022130
[454,] 3.961136 0.2722850 0.09381688 0.02742472
[455,] 4.128294 0.2434188 0.06973802 0.01910090
[456,] 4.387637 0.2593767 0.09186769 0.02824573
[457,] 4.220710 0.2828772 0.07329702 0.02190380
[458,] 4.241205 0.2408178 0.07597680 0.02686918
[459,] 3.741796 0.2667295 0.07881169 0.02014356
[460,] 4.282329 0.2851086 0.05755660 0.02250006
[461,] 3.990408 0.2290225 0.07623480 0.02277106
[462,] 4.406163 0.1879772 0.07118638 0.02700655
[463,] 4.350922 0.2697616 0.07079363 0.02410589
[464,] 4.316150 0.2429232 0.09442358 0.02339881
[465,] 4.001031 0.2650771 0.06018627 0.01930006
[466,] 4.545400 0.2062302 0.06625706 0.02457381
[467,] 3.741211 0.2103365 0.08370993 0.02407208
[468,] 3.840038 0.2185842 0.07904689 0.02993632
[469,] 4.221483 0.2738331 0.07777784 0.02655277
[470,] 4.347200 0.2686685 0.06700952 0.01899138
[471,] 4.093699 0.2368766 0.06396106 0.02159510
[472,] 4.067342 0.2410521 0.06238562 0.01710415
[473,] 4.407270 0.2502236 0.06104069 0.01872212
[474,] 3.469179 0.2205367 0.08266537 0.02526206
[475,] 3.936363 0.2498023 0.07880435 0.02412783
[476,] 4.753010 0.2545007 0.06541827 0.02112669
[477,] 4.596798 0.2169276 0.07594230 0.02502973
[478,] 4.087889 0.1767491 0.07158101 0.02406253
[479,] 4.168574 0.1963235 0.07039456 0.02196167
[480,] 4.526909 0.2280676 0.07878096 0.02070395
[481,] 4.363787 0.2791818 0.06819011 0.02260722
[482,] 4.202819 0.2421700 0.05946736 0.02087393
[483,] 4.056382 0.2913321 0.07738336 0.02004268
[484,] 3.989428 0.2750680 0.08569169 0.02342263
[485,] 3.958492 0.2447427 0.07223982 0.02153238
[486,] 4.136042 0.2598170 0.06871625 0.02646147
[487,] 4.454789 0.2591634 0.07936422 0.01880152
[488,] 4.094542 0.2292919 0.06301710 0.02334237
[489,] 4.512945 0.2435483 0.07772624 0.02309318
[490,] 3.814567 0.2030028 0.07701847 0.02159638
[491,] 4.423078 0.2252475 0.08471253 0.02182985
[492,] 4.284415 0.2102268 0.07666894 0.02737126
[493,] 3.849704 0.2085496 0.07058068 0.02123862
[494,] 3.994448 0.2623840 0.07620421 0.02411842
[495,] 4.105418 0.1853504 0.07208421 0.02059075
[496,] 4.236636 0.2036055 0.06800775 0.02306676
[497,] 4.331010 0.2385862 0.07455193 0.02193091
[498,] 3.650597 0.2918403 0.06538626 0.03138826
[499,] 4.071634 0.2213150 0.06797837 0.02306648
[500,] 3.847630 0.2160880 0.08819806 0.02605778
[501,] 4.088703 0.2672333 0.07411969 0.02318899
[502,] 4.338077 0.2227084 0.06476155 0.02181372
[503,] 4.271251 0.1880193 0.07695177 0.01913131
[504,] 4.085915 0.2557539 0.06839749 0.02155064
[505,] 4.160292 0.2470968 0.06650035 0.02508532
[506,] 4.201243 0.2187447 0.07743338 0.02128468
[507,] 3.965332 0.2162869 0.08001139 0.02642102
[508,] 4.084620 0.2474915 0.08032695 0.02084619
[509,] 3.888195 0.2164840 0.08169870 0.02534899
[510,] 4.107566 0.2452203 0.07108270 0.02132860
[511,] 3.987112 0.2139475 0.07822967 0.01840529
[512,] 4.184168 0.1919282 0.09447281 0.01901398
[513,] 4.382839 0.2010120 0.08444880 0.02324811
[514,] 4.165677 0.2310196 0.06700285 0.02144373
[515,] 3.913990 0.2567739 0.08216134 0.02821995
[516,] 4.349153 0.2455925 0.07044742 0.02169583
[517,] 4.243672 0.2039628 0.07721389 0.01818495
[518,] 4.194623 0.2468005 0.08613968 0.01976414
[519,] 4.318807 0.2747094 0.06379166 0.02594197
[520,] 3.773799 0.2207410 0.07571981 0.02876077
[521,] 4.004271 0.1698561 0.06608344 0.02266928
[522,] 3.829651 0.2638484 0.09136375 0.03024043
[523,] 4.317712 0.2084623 0.08689856 0.02693113
[524,] 4.521285 0.2553238 0.07315878 0.02203139
[525,] 3.823348 0.2210715 0.07501816 0.02137289
[526,] 4.430158 0.1972067 0.07641771 0.01888907
[527,] 4.361975 0.2521615 0.08921627 0.02355609
[528,] 4.253441 0.2598961 0.08850956 0.02741054
[529,] 3.986356 0.2271656 0.07823385 0.02079449
[530,] 4.208461 0.2596796 0.06667867 0.03264258
[531,] 4.333865 0.2652941 0.07369775 0.02408810
[532,] 4.360887 0.2632500 0.06631103 0.02410040
[533,] 3.645276 0.2739651 0.08499347 0.02200512
[534,] 3.913268 0.2075487 0.07035226 0.02105751
[535,] 3.934252 0.2190136 0.07202174 0.02207970
[536,] 3.950439 0.2283143 0.07533206 0.02377166
[537,] 3.885061 0.2283494 0.07260182 0.02349649
[538,] 3.992724 0.2280534 0.07296906 0.01741377
[539,] 4.186864 0.2320638 0.06074805 0.02706640
[540,] 4.253070 0.2090754 0.07890361 0.02447248
[541,] 3.898799 0.2049922 0.06474984 0.02388024
[542,] 4.304088 0.2505662 0.06395484 0.02290566
[543,] 4.073263 0.2719221 0.06132159 0.02356726
[544,] 4.130619 0.1547701 0.07240553 0.01794130
[545,] 4.094519 0.2184613 0.06680571 0.02230513
[546,] 3.853401 0.2129348 0.08518237 0.02370498
[547,] 4.265011 0.2679703 0.07216057 0.01872024
[548,] 4.344854 0.2502436 0.07501423 0.02098494
[549,] 4.292500 0.2185696 0.08353725 0.02699666
[550,] 4.370598 0.1925157 0.07577606 0.02004190
[551,] 4.040314 0.2873689 0.07957537 0.01754326
[552,] 4.471715 0.2304898 0.07401154 0.02703032
[553,] 4.047226 0.2295809 0.05938936 0.02233771
[554,] 4.379102 0.2290799 0.08006405 0.01880064
[555,] 3.837937 0.2340416 0.07181914 0.02155522
[556,] 3.967014 0.2200143 0.07545446 0.02054888
[557,] 4.459385 0.2449228 0.09224035 0.01668323
[558,] 4.248381 0.2786208 0.08140245 0.02731085
[559,] 3.788316 0.2656269 0.09633465 0.01665163
[560,] 3.847079 0.2017139 0.07762600 0.02175490
[561,] 4.215834 0.2343248 0.08342360 0.01962450
[562,] 3.887659 0.1607380 0.07180238 0.01846861
[563,] 4.113348 0.2643302 0.07607600 0.02445927
[564,] 4.194173 0.2634512 0.07588786 0.02272353
[565,] 4.001714 0.2278133 0.08079718 0.02256041
[566,] 4.720305 0.2357131 0.07847245 0.02151187
[567,] 4.194938 0.2631536 0.06223135 0.02413064
[568,] 3.895106 0.2244350 0.08724732 0.02144447
[569,] 3.969344 0.2944552 0.08473682 0.02149153
[570,] 4.318694 0.2252032 0.06441437 0.02833413
[571,] 3.940917 0.2161369 0.07584055 0.02384110
[572,] 4.501751 0.2584189 0.08590496 0.02804398
[573,] 3.913144 0.1875237 0.08571206 0.02139122
[574,] 4.001597 0.2729035 0.07102862 0.02725964
[575,] 4.061968 0.2664115 0.08120183 0.02338999
[576,] 3.823068 0.2749203 0.07393174 0.02538410
[577,] 4.105140 0.2614834 0.06586678 0.02625223
[578,] 4.236223 0.2413589 0.07727504 0.02124605
[579,] 3.984625 0.2661934 0.07207185 0.02215196
[580,] 4.160617 0.1931670 0.06797139 0.02456795
[581,] 3.692361 0.2291646 0.09036651 0.02120379
[582,] 4.189857 0.2491672 0.06367250 0.01913651
[583,] 4.170683 0.2665605 0.07760357 0.02650832
[584,] 4.579705 0.2861201 0.07711200 0.02284826
[585,] 4.036295 0.2427565 0.09060403 0.02188597
[586,] 4.233250 0.1973018 0.06909379 0.02180948
[587,] 3.796134 0.2046788 0.08560617 0.01846969
[588,] 4.170967 0.1924623 0.07578699 0.02009189
[589,] 3.970755 0.2371266 0.08279860 0.01991587
[590,] 4.294960 0.2291912 0.07245211 0.02118080
[591,] 4.043407 0.2355596 0.09688675 0.02607352
[592,] 4.025111 0.2532320 0.08700509 0.02418869
[593,] 4.755582 0.2476491 0.09390546 0.02387901
[594,] 4.433832 0.2230037 0.05799213 0.02345179
[595,] 4.123601 0.2561759 0.06863027 0.02130719
[596,] 3.985333 0.2926064 0.07538632 0.02488977
[597,] 4.279534 0.2457952 0.07500975 0.02641636
[598,] 4.072195 0.2525169 0.07300908 0.02127591
[599,] 4.084829 0.2160403 0.08054172 0.01826403
[600,] 4.723068 0.2396282 0.06961819 0.02154572
[601,] 4.206720 0.2434444 0.07942222 0.01914372
[602,] 4.096448 0.2096832 0.07943195 0.01759177
[603,] 4.201234 0.2562660 0.07284794 0.01876269
[604,] 4.131626 0.2245583 0.07501958 0.02024148
[605,] 4.195917 0.2355923 0.07435833 0.02321878
[606,] 4.414815 0.2237809 0.08421906 0.02809986
[607,] 3.973185 0.2400278 0.06748871 0.01854555
[608,] 4.636526 0.2867652 0.06360928 0.02152016
[609,] 3.971129 0.2422161 0.08211534 0.02311694
[610,] 4.144863 0.2004014 0.07621154 0.02487474
[611,] 3.722612 0.2461201 0.06155449 0.02293848
[612,] 4.145617 0.2406640 0.06748049 0.02559162
[613,] 4.104006 0.2585748 0.07728525 0.02623229
[614,] 4.472580 0.2433058 0.07598080 0.02575867
[615,] 4.627380 0.2560245 0.08108561 0.02580570
[616,] 4.338638 0.2931667 0.08017329 0.02143279
[617,] 4.375289 0.2421450 0.07868314 0.01963662
[618,] 3.930168 0.2246917 0.08499318 0.01930925
[619,] 4.818578 0.3280215 0.07079592 0.02840150
[620,] 4.068931 0.2315521 0.07489536 0.02019181
[621,] 3.908860 0.2530957 0.06414568 0.02114713
[622,] 4.377582 0.2449782 0.07204469 0.02384552
[623,] 3.789907 0.2930555 0.07381559 0.02157838
[624,] 4.231545 0.2508826 0.06222611 0.02422528
[625,] 4.275309 0.2432417 0.07220602 0.02234995
[626,] 3.859739 0.2035901 0.08565162 0.02032989
[627,] 4.263633 0.1870368 0.08228503 0.01896900
[628,] 4.346259 0.2713263 0.06837078 0.02190612
[629,] 4.291765 0.2489994 0.06963447 0.02671122
[630,] 4.346867 0.2280241 0.08304233 0.02542763
[631,] 4.209782 0.2829443 0.09360987 0.02733251
[632,] 4.068102 0.2447036 0.06766154 0.02184203
[633,] 4.456582 0.2823869 0.06999709 0.02124424
[634,] 3.879802 0.2324188 0.07128407 0.02047330
[635,] 3.901686 0.2690334 0.06300197 0.01795853
[636,] 4.025425 0.2512244 0.08415978 0.03085813
[637,] 3.887291 0.1739952 0.06755064 0.02252493
[638,] 4.489171 0.2887946 0.08440109 0.02664401
[639,] 3.702380 0.2079264 0.08293299 0.02715122
[640,] 4.011482 0.2235691 0.07161081 0.02239059
[641,] 4.221983 0.2568162 0.07211046 0.01805541
[642,] 4.006805 0.1966076 0.07718048 0.02070211
[643,] 4.454366 0.2574514 0.08563351 0.01698546
[644,] 4.285553 0.2365661 0.07630219 0.02121386
[645,] 4.139755 0.2389696 0.07210448 0.01749501
[646,] 4.215373 0.2697061 0.06468601 0.02395851
[647,] 4.528316 0.2549756 0.08565679 0.02570467
[648,] 4.770051 0.2235835 0.08060124 0.02381220
[649,] 3.996386 0.2531782 0.07088098 0.02253069
[650,] 4.357572 0.1930180 0.06710602 0.02498978
[651,] 4.016139 0.1943402 0.08651856 0.01964380
[652,] 4.156165 0.2431842 0.06096447 0.02209826
[653,] 4.194136 0.2324903 0.07166754 0.02026884
[654,] 4.192862 0.2078711 0.06431013 0.01731145
[655,] 4.444095 0.2369810 0.07176183 0.02576497
[656,] 4.073273 0.2097403 0.06839918 0.02689556
[657,] 3.950831 0.2233306 0.07918744 0.02007037
[658,] 3.885804 0.2102348 0.09089113 0.02879373
[659,] 4.010395 0.2597444 0.07745413 0.02148466
[660,] 3.570911 0.2400483 0.08969278 0.02144119
[661,] 3.645190 0.2228431 0.07135699 0.01480527
[662,] 3.796557 0.2239165 0.08928012 0.01741880
[663,] 3.983983 0.2467327 0.07873290 0.02208080
[664,] 3.807119 0.2206531 0.07752991 0.01930736
[665,] 4.566044 0.2642540 0.09398019 0.01770526
[666,] 4.193389 0.2928209 0.07116820 0.02374119
[667,] 4.212405 0.2357616 0.06788869 0.01857187
[668,] 3.916676 0.2861822 0.08706301 0.02623801
[669,] 4.080987 0.2380486 0.08098067 0.02149836
[670,] 4.432268 0.2719528 0.07103574 0.02138507
[671,] 4.188085 0.2536091 0.07161766 0.02409323
[672,] 3.934956 0.2809156 0.06579407 0.02497696
[673,] 4.044545 0.2304934 0.07002086 0.02390076
[674,] 4.152861 0.2707658 0.07911272 0.02544728
[675,] 4.429747 0.2602874 0.06512307 0.02352212
[676,] 3.964844 0.2403775 0.07616342 0.02182458
[677,] 3.607850 0.1801691 0.07352862 0.01899665
[678,] 4.537320 0.1955673 0.08254052 0.02078604
[679,] 4.465585 0.2354958 0.07638254 0.02320838
[680,] 4.091476 0.3193310 0.08495334 0.02248688
[681,] 4.481712 0.2263838 0.06739741 0.01923712
[682,] 4.080470 0.2384781 0.06822779 0.02440938
[683,] 4.635940 0.2645343 0.05566008 0.02305807
[684,] 3.762142 0.2539589 0.07670266 0.02208589
[685,] 3.865204 0.2203693 0.06476584 0.02478418
[686,] 3.996169 0.2323497 0.07684615 0.02166899
[687,] 4.119754 0.2377568 0.08666834 0.02070409
[688,] 4.263692 0.2209835 0.09595470 0.02228914
[689,] 4.265704 0.2746804 0.06444498 0.02587537
[690,] 4.463411 0.2473662 0.07789757 0.02627951
[691,] 3.954890 0.2696794 0.09584350 0.02356404
[692,] 3.998301 0.2181077 0.06793094 0.02137956
[693,] 4.131092 0.2295437 0.08157873 0.02004459
[694,] 4.961354 0.2325844 0.07705027 0.02715081
[695,] 4.429655 0.2146657 0.08492340 0.01965940
[696,] 4.373500 0.3297180 0.08041190 0.01907234
[697,] 3.956545 0.2433723 0.08578532 0.02498841
[698,] 4.271601 0.2034004 0.08133473 0.01625239
[699,] 4.184996 0.2464304 0.06158445 0.01981825
[700,] 3.987555 0.2616765 0.08059492 0.01916214
[701,] 4.241768 0.2751353 0.08810381 0.02299179
[702,] 3.963644 0.1906336 0.08010770 0.01987258
[703,] 4.313281 0.2338643 0.07068243 0.02554387
[704,] 4.583906 0.2635643 0.07798367 0.01758397
[705,] 4.163658 0.2459012 0.06357248 0.02274073
[706,] 4.118974 0.2374649 0.07577937 0.02297567
[707,] 3.892630 0.2393533 0.06855282 0.02821399
[708,] 3.877687 0.2611252 0.08147989 0.02367159
[709,] 4.737513 0.2606668 0.08240666 0.02633195
[710,] 4.047292 0.2186852 0.09528196 0.02435428
[711,] 4.156016 0.2233513 0.08458909 0.02595804
[712,] 4.723844 0.2792111 0.09373856 0.01824252
[713,] 4.351380 0.2196198 0.07341915 0.02868429
[714,] 4.109859 0.2520457 0.05724871 0.02569753
[715,] 3.835084 0.2161126 0.07932618 0.02280034
[716,] 3.986379 0.2774947 0.07875437 0.02333700
[717,] 3.888697 0.2591841 0.08378310 0.02078357
[718,] 4.193136 0.2767652 0.08654629 0.02420374
[719,] 4.436202 0.2530765 0.06104845 0.01708652
[720,] 4.354735 0.2008056 0.07837392 0.03048155
[721,] 4.182748 0.2466737 0.07597053 0.02628423
[722,] 3.999616 0.2771789 0.08559361 0.02294154
[723,] 4.240388 0.2411945 0.07761604 0.02394135
[724,] 4.412576 0.2185701 0.07519301 0.02777561
[725,] 4.102859 0.2230823 0.08827646 0.02298564
[726,] 4.056833 0.2795363 0.08341752 0.02734418
[727,] 3.971396 0.2299960 0.08094593 0.02319043
[728,] 4.114805 0.2378960 0.08202617 0.02633778
[729,] 4.593819 0.2573899 0.07655233 0.03110048
[730,] 3.816969 0.2025687 0.08309930 0.02745617
[731,] 4.336360 0.2963720 0.08024429 0.02505861
[732,] 4.230733 0.2548222 0.08893559 0.02050948
[733,] 4.217212 0.2653056 0.06439431 0.02703228
[734,] 4.158828 0.1877617 0.09751411 0.02413337
[735,] 4.076150 0.1854232 0.06305820 0.01841217
[736,] 4.328116 0.2340970 0.08651865 0.02809871
[737,] 4.374768 0.1697744 0.06291175 0.02238294
[738,] 4.347961 0.2229393 0.08722665 0.02798259
[739,] 4.163291 0.2070037 0.08711731 0.01741782
[740,] 4.231819 0.2071624 0.08003769 0.02235227
[741,] 4.185395 0.2422347 0.07049718 0.02034808
[742,] 4.141714 0.2210728 0.07403186 0.02122334
[743,] 4.189181 0.2188863 0.08424143 0.01874767
[744,] 4.325695 0.2836579 0.08619280 0.02407137
[745,] 4.182282 0.2658766 0.07007714 0.02514361
[746,] 3.940574 0.2620858 0.07812529 0.01858486
[747,] 3.474008 0.2154147 0.07057357 0.01937259
[748,] 3.927180 0.1943467 0.08772954 0.01871461
[749,] 3.816977 0.2236751 0.08536020 0.02393242
[750,] 4.239636 0.2082835 0.07620954 0.02333858
[751,] 3.872462 0.2428776 0.08426526 0.02260395
[752,] 4.282561 0.2481426 0.07284382 0.02122661
[753,] 4.324827 0.2276257 0.08468643 0.02150493
[754,] 4.312432 0.2261162 0.07659112 0.02579743
[755,] 4.029156 0.2253820 0.07593800 0.02036041
[756,] 4.380610 0.2647958 0.06879241 0.02168847
[757,] 4.109997 0.3375265 0.06994413 0.03213275
[758,] 3.899267 0.1829610 0.08150560 0.02045424
[759,] 4.182849 0.2848545 0.06398875 0.02081737
[760,] 3.689427 0.2160691 0.08546579 0.02739648
[761,] 3.992228 0.2371551 0.08157106 0.02063616
[762,] 4.226577 0.2539635 0.07390856 0.02042810
[763,] 4.740436 0.2486281 0.08349335 0.02267679
[764,] 4.484151 0.2086141 0.06721199 0.02133250
[765,] 4.110875 0.2612779 0.07182542 0.01744589
[766,] 3.876523 0.2229745 0.06433855 0.02087722
[767,] 4.601153 0.2582826 0.07906951 0.02131413
[768,] 4.262370 0.3251390 0.09151082 0.02774490
[769,] 3.895150 0.2237100 0.08037019 0.02180044
[770,] 4.256211 0.2118939 0.10106294 0.01896438
[771,] 4.026653 0.1780210 0.06577988 0.02873785
[772,] 3.999627 0.2479804 0.07146474 0.01960001
[773,] 3.937498 0.2359457 0.08878356 0.02184399
[774,] 4.416645 0.2984521 0.07094812 0.02275126
[775,] 4.258236 0.3038455 0.05886644 0.02095359
[776,] 4.054671 0.2616177 0.08292781 0.01976146
[777,] 3.806793 0.2655457 0.06972975 0.02175738
[778,] 4.236415 0.2739524 0.06964177 0.02293555
[779,] 4.379960 0.2690613 0.06983910 0.02548359
[780,] 4.057244 0.2731833 0.07261741 0.02743959
[781,] 4.427193 0.2435058 0.07080903 0.01804785
[782,] 3.879994 0.1696443 0.06428235 0.02505980
[783,] 4.001476 0.2772659 0.07319260 0.02045918
[784,] 3.479319 0.2169341 0.08255637 0.02731686
[785,] 3.994919 0.2969814 0.07859549 0.01955086
[786,] 4.542809 0.2356319 0.07946277 0.02048460
[787,] 3.790099 0.2435416 0.07185682 0.02582604
[788,] 4.311546 0.2753494 0.07679862 0.02861077
[789,] 4.143562 0.2198720 0.07841386 0.01991693
[790,] 3.996685 0.2252054 0.06833739 0.01874148
[791,] 3.927491 0.1909402 0.08463335 0.02860073
[792,] 3.883780 0.2264328 0.08162959 0.02349270
[793,] 4.359099 0.2191319 0.08944932 0.02272764
[794,] 4.133957 0.2694238 0.06918560 0.02340639
[795,] 4.270195 0.2239822 0.08315739 0.02501109
[796,] 4.105217 0.2569533 0.08126683 0.02126235
[797,] 4.049475 0.2339489 0.06190168 0.02116490
[798,] 3.660463 0.2337050 0.06986532 0.02696719
[799,] 4.742458 0.2557218 0.08186518 0.01728269
[800,] 3.888632 0.2846851 0.07829192 0.02187778
[801,] 4.189313 0.2423964 0.07162977 0.02166635
[802,] 4.147506 0.1846200 0.07295027 0.02458495
[803,] 4.001312 0.2232140 0.06295736 0.02482196
[804,] 3.990665 0.1808793 0.08053047 0.02005502
[805,] 4.125479 0.2036522 0.06716814 0.01817954
[806,] 3.874359 0.2634153 0.07084627 0.02624613
[807,] 3.955202 0.2788028 0.07804799 0.02732746
[808,] 4.349373 0.2591353 0.07220047 0.02077857
[809,] 3.943617 0.3092590 0.07455877 0.02147141
[810,] 4.145949 0.1829250 0.05888538 0.02155862
[811,] 3.891224 0.2509646 0.08315076 0.01847186
[812,] 4.236887 0.2391303 0.08969682 0.02087816
[813,] 4.225390 0.2348356 0.07068723 0.02291353
[814,] 3.585705 0.1892000 0.08629609 0.01876974
[815,] 4.403605 0.2062500 0.08057538 0.01725438
[816,] 4.382015 0.2596891 0.08999266 0.02436910
[817,] 4.372209 0.2958549 0.06466449 0.02909327
[818,] 3.533922 0.2240189 0.08259071 0.02937086
[819,] 4.090517 0.2192571 0.04817138 0.02018827
[820,] 4.052504 0.2869060 0.04746258 0.02527766
[821,] 3.717708 0.2040233 0.07876831 0.02591374
[822,] 4.702359 0.2132020 0.07502849 0.02512004
[823,] 4.326919 0.2577886 0.07119235 0.02729569
[824,] 4.157994 0.2321716 0.07565182 0.03087519
[825,] 3.696699 0.2298341 0.07097235 0.02158715
[826,] 3.998556 0.2202271 0.08653753 0.02066749
[827,] 4.098236 0.1963866 0.05993080 0.02302706
[828,] 4.182824 0.2771057 0.07461653 0.02048808
[829,] 4.424241 0.2645369 0.07405102 0.02255324
[830,] 3.635927 0.2258247 0.09263375 0.02291120
[831,] 3.553681 0.2346405 0.09266132 0.01891833
[832,] 3.951594 0.2489431 0.10066648 0.02256259
[833,] 3.786088 0.2772098 0.08773131 0.03002936
[834,] 4.403257 0.2000012 0.07096009 0.02788180
[835,] 4.086382 0.2843444 0.06802735 0.02271977
[836,] 4.033756 0.2219133 0.07617760 0.02613717
[837,] 4.273327 0.2705339 0.08110326 0.02483847
[838,] 3.469193 0.2442335 0.07152163 0.02733613
[839,] 4.475439 0.2221864 0.06627792 0.01845387
[840,] 3.608184 0.2839314 0.08010060 0.03005575
[841,] 3.955984 0.2386882 0.08027646 0.03301122
[842,] 3.797506 0.2243604 0.07420955 0.02315303
[843,] 4.722879 0.2319277 0.08164720 0.02222050
[844,] 4.240827 0.2924592 0.06592270 0.02110716
[845,] 3.688350 0.2118373 0.06835405 0.02482173
[846,] 4.090402 0.2787215 0.07575405 0.02401716
[847,] 4.805716 0.2348876 0.07939500 0.02139094
[848,] 4.276048 0.2355720 0.06990536 0.02453285
[849,] 4.262367 0.1853872 0.07978153 0.02311025
[850,] 4.120493 0.2455411 0.10068506 0.02195033
[851,] 4.149425 0.2343776 0.07176334 0.01906668
[852,] 3.960707 0.2281225 0.06678002 0.02479461
[853,] 4.335981 0.2155091 0.06192252 0.02329311
[854,] 4.289008 0.2494317 0.08446102 0.02682920
[855,] 3.936171 0.1928334 0.08997093 0.02621127
[856,] 4.704068 0.2699636 0.06898057 0.02235533
[857,] 4.212430 0.2191249 0.08286116 0.01978217
[858,] 3.968019 0.2845027 0.08964717 0.02301573
[859,] 4.057207 0.2534308 0.07446037 0.02323627
[860,] 4.586395 0.2415302 0.07792868 0.02202104
[861,] 4.528601 0.2353373 0.07673187 0.02147860
[862,] 4.455945 0.2852247 0.06418872 0.01988471
[863,] 4.347291 0.2263864 0.06893955 0.01787710
[864,] 4.372266 0.1858774 0.07337689 0.01784412
[865,] 4.369598 0.2392257 0.06500319 0.03032204
[866,] 4.115175 0.2374966 0.06741848 0.02078513
[867,] 4.406181 0.2728176 0.07392128 0.02384434
[868,] 4.266494 0.2159662 0.07146428 0.02654037
[869,] 4.370769 0.2502234 0.08653634 0.02419666
[870,] 4.854574 0.2679640 0.07085932 0.02383350
[871,] 4.404602 0.2748034 0.07177789 0.02688787
[872,] 4.249973 0.3144284 0.07028295 0.01784612
[873,] 4.224799 0.2009915 0.09693983 0.02375911
[874,] 4.439439 0.1840650 0.07283837 0.03242106
[875,] 4.690082 0.2168559 0.06441288 0.02565548
[876,] 3.836297 0.2180523 0.06857039 0.02672767
[877,] 4.594749 0.2101872 0.07896719 0.02241271
[878,] 4.588508 0.2305306 0.07614417 0.02305972
[879,] 3.750283 0.2820230 0.06429545 0.02442790
[880,] 4.068753 0.2500049 0.08707083 0.02230317
[881,] 4.121486 0.1945073 0.06975492 0.02539538
[882,] 4.384702 0.2107849 0.08567317 0.02052339
[883,] 3.889924 0.2076474 0.06835513 0.01867881
[884,] 4.065393 0.1787418 0.08159879 0.02469670
[885,] 3.991092 0.2431648 0.07239291 0.02087523
[886,] 3.871421 0.1907575 0.07988996 0.02018640
[887,] 4.298798 0.2550689 0.06630583 0.02439834
[888,] 4.559801 0.2658973 0.06429957 0.02333946
[889,] 4.642910 0.2060396 0.07832347 0.02169991
[890,] 4.273373 0.2738088 0.06719847 0.02726587
[891,] 4.156491 0.2686396 0.08340152 0.02449549
[892,] 4.135386 0.2718620 0.07294651 0.02429846
[893,] 4.279915 0.2345069 0.07408656 0.02195890
[894,] 3.911005 0.2222004 0.07687739 0.01935952
[895,] 4.346238 0.2765215 0.06997448 0.01926761
[896,] 3.995816 0.2310198 0.08560606 0.02461240
[897,] 4.375702 0.2454015 0.07434960 0.02383618
[898,] 4.307348 0.2262874 0.09923838 0.02056982
[899,] 4.186182 0.2429121 0.09211524 0.01891870
[900,] 4.587760 0.2517381 0.06788277 0.02700452
[901,] 3.970345 0.2330951 0.08428632 0.02537285
[902,] 4.647743 0.2272406 0.08660582 0.02072607
[903,] 4.216520 0.2433561 0.08630495 0.02312747
[904,] 3.991130 0.2663937 0.08758302 0.01807963
[905,] 3.939817 0.2731304 0.09182095 0.02253553
[906,] 4.036889 0.2416421 0.06952929 0.02075517
[907,] 4.685533 0.2248881 0.08572503 0.01830280
[908,] 4.198501 0.2202087 0.09429860 0.02483403
[909,] 4.097057 0.1785831 0.07831439 0.02601218
[910,] 4.387845 0.2321262 0.07411299 0.02175828
[911,] 4.116090 0.2831442 0.07941757 0.02151569
[912,] 4.190063 0.1901312 0.08770791 0.02998459
[913,] 4.053614 0.2286139 0.09468544 0.02202445
[914,] 4.302475 0.2101613 0.05618263 0.02478746
[915,] 4.419800 0.1978945 0.08076538 0.02231084
[916,] 3.944370 0.1912324 0.08430115 0.02458049
[917,] 4.103549 0.2425736 0.08164634 0.02475424
[918,] 4.003802 0.2154694 0.07167657 0.02325375
[919,] 4.028198 0.2206548 0.08385304 0.02348990
[920,] 4.304295 0.1931861 0.07722058 0.01899198
[921,] 4.381344 0.2997668 0.06476283 0.02106419
[922,] 4.334740 0.1855024 0.09100084 0.02025896
[923,] 4.523925 0.2331456 0.08274057 0.02400682
[924,] 3.888117 0.2591270 0.10016111 0.02841966
[925,] 4.140910 0.2613666 0.06510896 0.01898636
[926,] 4.095025 0.2822531 0.06800665 0.02457552
[927,] 4.471822 0.2226513 0.07722901 0.03175347
[928,] 4.132450 0.2991787 0.06607805 0.01858488
[929,] 4.094719 0.2100590 0.07664180 0.02690267
[930,] 3.968725 0.2505510 0.07238277 0.02237592
[931,] 4.268252 0.2492490 0.07612965 0.01988264
[932,] 4.231183 0.3015731 0.08686103 0.02355357
[933,] 4.054686 0.2046908 0.07353999 0.02632891
[934,] 4.786044 0.2601203 0.06952081 0.02435328
[935,] 4.249978 0.2632130 0.07442567 0.01787872
[936,] 4.441979 0.2307787 0.07666076 0.02764592
[937,] 4.434788 0.2715058 0.07373083 0.02112839
[938,] 3.967740 0.2002808 0.07772190 0.02202826
[939,] 4.639137 0.2671976 0.08352915 0.02376852
[940,] 4.152366 0.2811793 0.05559945 0.02383914
[941,] 4.181864 0.2890590 0.08222539 0.02576776
[942,] 4.335474 0.2132023 0.06021891 0.02154434
[943,] 4.058896 0.2572243 0.06660544 0.01989867
[944,] 4.256658 0.2502787 0.06498967 0.02662068
[945,] 4.588296 0.2227304 0.07091389 0.02074479
[946,] 4.046259 0.2733541 0.08494109 0.02640708
[947,] 4.118800 0.2831441 0.07696010 0.02267377
[948,] 4.130468 0.2556125 0.08728943 0.01924192
[949,] 4.451994 0.1953858 0.06825316 0.02689807
[950,] 4.916602 0.2353336 0.08202410 0.02321662
[951,] 4.696307 0.2670447 0.08580561 0.01912413
[952,] 4.421731 0.2259308 0.07304431 0.02302850
[953,] 4.070655 0.1887539 0.08225829 0.02369980
[954,] 4.493708 0.2941846 0.05783497 0.02314802
[955,] 4.435809 0.2240273 0.08848072 0.02427533
[956,] 4.239569 0.2426022 0.07529953 0.02338881
[957,] 4.257666 0.2940446 0.06041303 0.02394010
[958,] 3.922767 0.2294421 0.08415868 0.02196453
[959,] 4.180625 0.2669743 0.06996385 0.02404609
[960,] 4.366167 0.2662950 0.07335837 0.02103100
[961,] 4.035621 0.2342260 0.07450713 0.02413947
[962,] 4.171314 0.2273395 0.07389771 0.02307078
[963,] 4.351481 0.2523674 0.07625104 0.02101317
[964,] 3.948570 0.2034211 0.08123933 0.02652876
[965,] 4.335931 0.2160882 0.07290419 0.02750383
[966,] 4.405045 0.2724213 0.07742490 0.01799766
[967,] 3.931064 0.2305843 0.06938529 0.02347720
[968,] 3.814160 0.2539825 0.08737315 0.02626460
[969,] 3.865164 0.1984016 0.06832634 0.02685192
[970,] 4.167760 0.2644865 0.06700970 0.02029449
[971,] 3.630513 0.2881710 0.07254820 0.03102168
[972,] 3.841252 0.2110838 0.05835012 0.01871034
[973,] 4.404949 0.2035457 0.07586407 0.01949212
[974,] 4.396228 0.2243307 0.08125964 0.02651710
[975,] 4.514115 0.2293425 0.08457013 0.02280119
[976,] 3.863457 0.1732843 0.07127497 0.02064052
[977,] 4.470745 0.2278160 0.07543510 0.02836837
[978,] 3.942854 0.2986321 0.07050106 0.02053073
[979,] 4.499996 0.2639942 0.07158241 0.01934189
[980,] 4.279122 0.2405436 0.07662956 0.02909570
[981,] 4.060468 0.2267262 0.08205470 0.02286632
[982,] 4.423022 0.2928719 0.07303776 0.02245727
[983,] 4.206544 0.1996476 0.07341453 0.01888254
[984,] 3.869540 0.2347236 0.06009160 0.02133484
[985,] 4.367671 0.2414356 0.06839577 0.02857875
[986,] 4.018440 0.1816354 0.08329595 0.02506999
[987,] 4.143246 0.2096917 0.08252218 0.02503675
[988,] 4.232941 0.2275382 0.08993687 0.02220287
[989,] 4.419365 0.2238542 0.07700252 0.03122118
[990,] 4.083620 0.2198357 0.06555678 0.01771009
[991,] 3.777667 0.2810658 0.06277355 0.02577740
[992,] 3.998002 0.2393079 0.07775492 0.02204900
[993,] 3.932904 0.2308459 0.06495352 0.01935282
[994,] 4.296648 0.2455460 0.07005929 0.02209757
[995,] 4.141908 0.3093720 0.08606012 0.02346604
[996,] 4.085976 0.2431552 0.07619191 0.01865958
[997,] 4.081344 0.2160935 0.09243889 0.02562543
[998,] 4.125323 0.2009691 0.06922495 0.01918178
[999,] 4.398971 0.2401103 0.07650688 0.02465242
[1000,] 3.992960 0.2949924 0.07070691 0.02466306
function (valores, size = 1000, alpha = 0.05, plot = TRUE)
{
if (is.matrix(valores) == FALSE) {
return("Oject is not a matrix")
}
else {
lengs = length(valores[, 1])
hlengs = length(valores[1, ])
store_bootstrap = matrix(0, size, hlengs)
elements_aux = NULL
indexes = seq(1, lengs, 1)
work_matrix = matrix(0, lengs, hlengs)
empirical_quantiles1 = matrix(0, hlengs - 1, 2)
store_eigen = matrix(0, size, hlengs)
empirical_quantiles2 = matrix(0, hlengs, 2)
for (sim in 1:size) {
resample_indexes = sample(indexes, length(indexes),
replace = T)
for (ips in 1:length(resample_indexes)) {
work_matrix[ips, ] = valores[resample_indexes[ips],
]
}
cova = (lengs - 1) * cov(work_matrix)/(lengs)
auto_va = unlist(eigen(cova)$values)
cum_eigen = cumsum(auto_va)
total_var = sum(auto_va)
percent = (cum_eigen/total_var)
store_bootstrap[sim, ] = percent
store_eigen[sim, ] = auto_va
}
store_bootstrap = store_bootstrap[, -hlengs]
for (iter in 1:(hlengs - 1)) {
empirical_quantiles1[iter, 2] = quantile(store_bootstrap[,
iter], 1 - alpha/2)
empirical_quantiles1[iter, 1] = quantile(store_bootstrap[,
iter], alpha/2)
}
for (iter in 1:(hlengs)) {
empirical_quantiles2[iter, 2] = quantile(store_eigen[,
iter], 1 - alpha/2)
empirical_quantiles2[iter, 1] = quantile(store_eigen[,
iter], alpha/2)
}
if (plot == TRUE) {
plot(0:max(empirical_quantiles2[, 2]), 0:max(empirical_quantiles2[,
2]), xlim = c(0, max(empirical_quantiles2)),
ylim = c(0, nrow(empirical_quantiles2)), type = "n",
xlab = "Values", ylab = "Eigenvalues")
for (q in 1:nrow(empirical_quantiles2)) {
segments(empirical_quantiles2[q, 1], q, empirical_quantiles2[q,
2], q, lwd = 2)
abline(v = empirical_quantiles2[q, 1], lty = 3)
}
}
colnames(empirical_quantiles1) = c(paste(alpha/2 * 100,
"%"), paste((1 - alpha/2) * 100, "%"))
colnames(empirical_quantiles2) = c(paste(alpha/2 * 100,
"%"), paste((1 - alpha/2) * 100, "%"))
lista = list(proportions_quantiles = empirical_quantiles1,
proportions_used = store_bootstrap, eigen_quantiles = empirical_quantiles2,
eigen_used = store_eigen)
return(lista)
}
}
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