Informe 2
María José Reina
2023-09-17
##Problema 2: La simulación ayuda a entender y validar las propiedades de los estimadores estadísticos como son insesgadez, eficiencia y la consistencia principalmente. El siguiente problema permite evidenciar las principales características de un grupo de estimadores propuestos para la estimación de un parámetro asociado a un modelo de probabilidad.
Sean X1, X2, X3 y X4, una muestra aleatoria de tamaño n=4 cuya población la conforma una distribución exponencial con parámetro θ desconocido. Determine las características de cada uno de los siguientes estimadores propuestos:
Para n = 4
library(ggplot2)
x=matrix(data=rexp(1000*4,rate=1), nrow=1000, byrow=TRUE)
x4=x[1:4,]
estimador1 <- function(x4) {
estimador_1 <-((x4[1]+x4[2])/6) + ((x4[3]+x4[4]) / 3)
}
estimador2 <- function(x4) {
estimador_2 <-((x4[1]+(2*(x4[2]))+(3*x4[3])+(4*x4[4]))/5)
}
estimador3 <- function(x4) {
estimador_3 <-((x4[1]+x4[2]+x4[3]+x4[4])/4)
}
estimador4 <- function(x4) {
estimador_4 <-((min(x4[1],x4[2],x4[3],x4[4]))+(max(x4[1],x4[2],x4[3],x4[4]))/2)
}
for (i in 1:4){
est1 <- apply(x4, 1, estimador1)
est2<-apply(x4, 1, estimador2)
est3<-apply(x4, 1, estimador3)
est4<-apply(x4, 1, estimador4)
results<-data.frame(Estimador1 =est1, Estimador2= est2, Estimador3 = est3, Estimador4 = est4)
}
print(results)## Estimador1 Estimador2 Estimador3 Estimador4
## 1 0.8358688 1.435377 1.1810765 1.4528578
## 2 0.4575049 1.056582 0.5774945 0.9809568
## 3 1.0280816 2.001385 0.8777600 1.3757767
## 4 0.6720405 1.488660 0.5717307 0.9034168boxplot(results, las=1, main="Comparación estimadores con n=4", col = c("green","yellow","purple","blue"), names = c("Estimador1","Estimador2","Estimador3","Estimador4"))
abline(h=1, col="red") 
apply (results,2,mean)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.7483740 1.4955010 0.8020154 1.1782520apply(results,2,var)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.05877444 0.15074317 0.08428842 0.07629471Para un tamaño de muesta n=4 se observa que los mejores resultados se obtienen con el Estimador3, el cual se puede clasificar como Insesgado y Eficiente, ya que su promedio esta muy cercano a 1 y es aquel que presenta una varianza menor.
Para n = 20
x=matrix(data=rexp(1000*4,rate=1), nrow=1000, byrow=TRUE)
x20=x[1:20,]
estimador1 <- function(x20) {
estimador_1 <-((x20[1]+x20[2])/6) + ((x20[3]+x20[4]) / 3)
}
estimador2 <- function(x20) {
estimador_2 <-((x20[1]+(2*(x20[2]))+(3*x20[3])+(4*x20[4]))/5)
}
estimador3 <- function(x20) {
estimador_3 <-((x20[1]+x20[2]+x20[3]+x20[4])/4)
}
estimador4 <- function(x20) {
estimador_4 <-((min(x20[1],x20[2],x20[3],x20[4]))+(max(x20[1],x20[2],x20[3],x20[4]))/2)
}
for (i in 1:20){
est1 <- apply(x20, 1, estimador1)
est2<-apply(x20, 1, estimador2)
est3<-apply(x20, 1, estimador3)
est4<-apply(x20, 1, estimador4)
results<-data.frame(Estimador1 =est1, Estimador2= est2, Estimador3 = est3, Estimador4 = est4)
}
print(results)## Estimador1 Estimador2 Estimador3 Estimador4
## 1 0.3144820 0.4776233 0.3662071 0.4878373
## 2 1.0497190 2.0337272 0.7945533 1.2275275
## 3 0.9121836 2.1764247 1.0940164 1.6536061
## 4 0.4113500 0.9626884 0.3386010 0.5683635
## 5 0.6346116 1.1323313 0.5842231 0.7347657
## 6 1.3914783 2.5962675 1.3699762 1.5519164
## 7 0.5091126 1.0357837 0.5182833 0.7701761
## 8 0.8567091 1.7270627 0.6994127 0.8417500
## 9 0.4954180 0.9024035 0.4950120 0.5145023
## 10 0.6517771 1.3154303 0.7144420 0.9955676
## 11 0.5507506 1.1652168 0.5614000 0.7335180
## 12 0.4362850 0.8895316 0.3832983 0.4058798
## 13 0.7072252 1.3278782 0.7229802 0.7723205
## 14 0.5023634 0.8263715 0.6777993 0.9725421
## 15 0.5990601 1.1269918 0.5238592 0.8310507
## 16 0.4615221 0.9672866 0.4473662 0.6554688
## 17 0.4672863 0.9561658 0.4780778 0.5448841
## 18 0.8349214 1.8997068 0.7315449 1.1673901
## 19 0.8566794 1.9097793 1.0563777 1.6780592
## 20 0.8005351 1.4436302 0.7793155 0.8409604boxplot(results, las=1, main="Comparación estimadores con n=20", col = c("green","yellow","purple","blue"), names = c("Estimador1","Estimador2","Estimador3","Estimador4") )
abline(h=1, col="red") 
apply (results,2,mean)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.6721735 1.3436151 0.6668373 0.8974043apply(results,2,var)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.06717811 0.29474536 0.06950864 0.14471898Para un tamaño de muesta n=20, se observa que al igual que n=4 los mejores resultados se obtienen con el Estimador3, el cual se puede clasificar como Insesgado y Eficiente, ya que su promedio esta muy cercano a 1 y es aquel que presenta una varianza menor, sin embargo el Estimador 1 también se podría considerar Insesgado y eficiente ya que sus resultados se asemejan al Estimador3.
Para n = 50
x=matrix(data=rexp(1000*4,rate=1), nrow=1000, byrow=TRUE)
x50=x[1:50,]
estimador1 <- function(x50) {
estimador_1 <-((x50[1]+x50[2])/6) + ((x50[3]+x50[4]) / 3)
}
estimador2 <- function(x50) {
estimador_2 <-((x50[1]+(2*(x50[2]))+(3*x50[3])+(4*x50[4]))/5)
}
estimador3 <- function(x50) {
estimador_3 <-((x50[1]+x50[2]+x50[3]+x50[4])/4)
}
estimador4 <- function(x50) {
estimador_4 <-((min(x50[1],x50[2],x50[3],x50[4]))+(max(x50[1],x50[2],x50[3],x50[4]))/2)
}
for (i in 1:50){
est1 <- apply(x50, 1, estimador1)
est2<-apply(x50, 1, estimador2)
est3<-apply(x50, 1, estimador3)
est4<-apply(x50, 1, estimador4)
results<-data.frame(Estimador1 =est1, Estimador2= est2, Estimador3 = est3, Estimador4 = est4)
}
print(results)## Estimador1 Estimador2 Estimador3 Estimador4
## 1 1.2040444 2.6448736 1.5411978 2.5087168
## 2 0.6952865 1.3520079 0.7974517 0.9718685
## 3 1.6568301 3.1339299 1.4448016 2.3278432
## 4 0.9547693 1.7014743 0.9735241 1.1748739
## 5 0.6920920 1.2001455 0.9076258 1.1170014
## 6 0.5436446 0.9367233 0.6224738 0.9931343
## 7 1.2039438 2.3930718 1.1524551 1.3698217
## 8 0.9216144 1.5010117 1.0942756 1.7048625
## 9 1.0672315 1.8917470 1.0241696 0.9137222
## 10 0.2044268 0.4109066 0.2420384 0.2824693
## 11 0.7490221 1.6805408 0.7393804 0.8574975
## 12 0.7620690 1.4208355 0.6492787 1.0910041
## 13 0.9899453 2.0823797 0.8062803 0.9637034
## 14 1.9652464 2.7371904 2.5540920 4.3385673
## 15 0.3008742 0.6585133 0.3932600 0.6060225
## 16 1.6628028 3.3595816 1.7368979 2.1769690
## 17 1.7708570 3.8259214 1.6482811 2.2227968
## 18 1.3351350 2.3419904 1.3161199 1.2718105
## 19 2.1409803 3.8342328 2.1533996 2.4066361
## 20 1.1277044 2.1974654 1.0162089 1.5972321
## 21 0.6327989 1.1189232 0.7024646 0.5362699
## 22 2.0388747 4.7136001 1.7640747 2.6546647
## 23 0.2220054 0.4783826 0.2638868 0.3902858
## 24 0.5462555 1.0309693 0.6404935 0.6030817
## 25 0.8421529 1.7525860 0.9145885 1.0034911
## 26 0.2490365 0.4235465 0.3175043 0.3292475
## 27 0.5038910 0.9636045 0.4222978 0.6928009
## 28 1.8162928 3.8996478 1.7398802 2.3224611
## 29 2.3572431 5.1743861 1.8920563 2.6443933
## 30 0.6157283 1.2209800 0.5854359 0.6430468
## 31 0.5593336 0.9036942 0.6844947 0.8682046
## 32 0.6330934 1.0913860 0.7883299 1.1491619
## 33 0.7538313 1.7392322 0.6115209 1.0958504
## 34 1.6117797 2.7621403 1.7925485 2.6912652
## 35 0.2182162 0.4709470 0.2985838 0.4817611
## 36 0.6033827 1.3288778 0.5974801 0.6030410
## 37 1.5174900 2.3735668 1.9600463 3.4172914
## 38 0.4226964 0.9456487 0.5633494 1.0087513
## 39 0.2418489 0.4736271 0.2866656 0.3172673
## 40 0.9239138 1.6127781 1.0446873 1.4883294
## 41 0.1320983 0.2779391 0.1115048 0.1289443
## 42 1.4547974 2.8586221 1.7802546 1.6575805
## 43 1.7160704 3.4993866 1.4894431 1.7303344
## 44 0.9658266 1.5835905 1.0731506 1.4670658
## 45 0.1989048 0.4183864 0.1830203 0.1864062
## 46 1.3785331 2.8109770 1.2134253 1.2276807
## 47 0.1881727 0.4043453 0.1901688 0.2015835
## 48 0.8355569 1.4910919 0.8916713 1.2562161
## 49 0.2510311 0.5299453 0.2381616 0.2244149
## 50 1.3382067 2.1232115 1.8277739 2.6182606boxplot(results, las=1, main="Comparación estimadores con n=50", col = c("green","yellow","purple","blue"), names = c("Estimador1","Estimador2","Estimador3","Estimador4"))
abline(h=1, col="red") 
apply (results,2,mean)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.9543517 1.8356113 0.9936435 1.3307141apply(results,2,var)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.3532016 1.4250597 0.3642768 0.8461778Para un tamaño de muesta n=100, se observa nuevamente el Estimador3, este estimador se puede clasificar como INSESGADO, pues su promedio está más cercano a 1 pero no EFICIENTE, ya que el estimador que tiene la menor varianza es el Estimador1.
Para n = 100
x=matrix(data=rexp(1000*4,rate=1), nrow=1000, byrow=TRUE)
x100=x[1:100,]
estimador1 <- function(x100) {
estimador_1 <-((x100[1]+x100[2])/6) + ((x100[3]+x100[4]) / 3)
}
estimador2 <- function(x100) {
estimador_2 <-((x100[1]+(2*(x100[2]))+(3*x100[3])+(4*x100[4]))/5)
}
estimador3 <- function(x100) {
estimador_3 <-((x100[1]+x100[2]+x100[3]+x100[4])/4)
}
estimador4 <- function(x100) {
estimador_4 <-((min(x100[1],x100[2],x100[3],x100[4]))+(max(x100[1],x100[2],x100[3],x100[4]))/2)
}
for (i in 1:100){
est1 <- apply(x100, 1, estimador1)
est2<-apply(x100, 1, estimador2)
est3<-apply(x100, 1, estimador3)
est4<-apply(x100, 1, estimador4)
results<-data.frame(Estimador1 =est1, Estimador2= est2, Estimador3 = est3, Estimador4 = est4)
}
print(results)## Estimador1 Estimador2 Estimador3 Estimador4
## 1 2.4714781 5.1193302 1.8688367 2.0582037
## 2 1.9494210 4.0732047 1.8427680 2.7101190
## 3 0.6936926 1.4818785 0.6738514 0.8950918
## 4 1.5237723 2.9747825 1.6878254 1.8663891
## 5 1.9807196 3.6369734 1.9436372 2.5580906
## 6 1.4232661 3.1945682 1.5918630 2.3279928
## 7 0.9207497 1.4545220 1.1867728 2.0201746
## 8 0.7406991 1.1700029 0.9330351 1.5580150
## 9 0.5859289 1.3246596 0.7443704 1.2558331
## 10 1.0824664 2.2422148 1.2743440 1.9285527
## 11 1.1643971 2.2440051 1.1128829 0.9878090
## 12 0.5074954 1.0894568 0.4412314 0.5964765
## 13 1.2330113 2.1158202 1.5844459 2.1306207
## 14 0.2357644 0.4083538 0.2916402 0.4079789
## 15 1.8677379 3.9228516 1.6650641 1.6154017
## 16 1.2645842 2.2905735 1.2667744 1.5625767
## 17 0.9180714 1.8693203 0.9017557 1.0311925
## 18 1.2656161 2.5720757 1.1474325 1.3712699
## 19 0.8410968 1.8082210 0.9415320 1.4446939
## 20 2.0375655 4.4110535 1.9485191 1.8891532
## 21 1.0555010 2.3224304 0.9283656 1.4807604
## 22 0.4018171 0.8683366 0.3911653 0.4441699
## 23 0.3517765 0.7498227 0.4268435 0.6883811
## 24 1.2303161 2.4659445 1.0431296 1.2198016
## 25 0.6095073 1.3330107 0.5552991 0.5174558
## 26 1.4325334 2.6504436 1.2431030 1.9478511
## 27 1.4777223 2.6375586 1.9409938 1.7820859
## 28 1.2433282 2.6967254 1.0122400 1.4078641
## 29 1.7758918 3.7618280 1.4651257 1.9125729
## 30 2.6324456 4.8561490 2.2039520 3.8370635
## 31 1.6211008 3.4414219 1.5178984 1.7818349
## 32 0.7884072 1.6494183 0.8240039 1.2191698
## 33 0.4548402 0.9305902 0.5615484 0.8222033
## 34 0.8026510 1.4497111 0.8001225 0.9540642
## 35 1.4961944 2.6898696 1.3884632 1.9234752
## 36 1.8713380 4.1245611 1.7125159 2.5853440
## 37 1.3112414 2.1319524 1.5673667 2.4283222
## 38 0.9145069 1.7710226 1.0184034 1.2780500
## 39 0.9012174 1.7541214 0.8399738 1.2989855
## 40 0.5624547 1.1019431 0.5888780 0.8584305
## 41 1.0627120 1.8951727 0.9285764 1.3868132
## 42 2.3487667 5.5093683 2.0044353 3.1936360
## 43 0.4594172 0.9621778 0.4406757 0.6608358
## 44 2.8457765 6.3758801 2.9339245 3.6512412
## 45 0.5986026 1.3466426 0.5252045 0.5700601
## 46 0.7232509 1.3620498 0.8488706 1.1102109
## 47 0.3357636 0.5503030 0.4462659 0.6702942
## 48 1.2194502 2.1799000 1.6275063 1.9555139
## 49 1.6155132 3.5084253 1.5871182 1.6366798
## 50 1.5071150 2.7428387 1.7255607 2.4043251
## 51 0.7238889 1.4659785 0.7621513 0.9098236
## 52 1.5077607 3.3902170 1.5179158 1.4973140
## 53 1.5140320 2.9722690 1.4690350 1.7957605
## 54 0.4057281 0.8380211 0.4479043 0.6060309
## 55 0.8085260 1.7328672 0.7593557 0.8406861
## 56 1.2235508 2.5217116 1.2489075 1.5504771
## 57 0.5235910 1.0936214 0.4125207 0.4314627
## 58 1.0400550 2.3113452 0.8872745 1.3227571
## 59 1.5188705 3.1719861 1.4935354 1.8910682
## 60 0.8270477 1.5394063 0.7511041 1.0842136
## 61 1.5659021 3.1717924 1.2925856 1.6569219
## 62 0.7018133 1.6605327 0.9940079 1.8772056
## 63 0.5471456 1.2279669 0.6077641 0.8259277
## 64 0.1978453 0.3460265 0.2429315 0.3510618
## 65 1.0934079 2.2422216 0.9395418 1.0591475
## 66 1.5023918 3.1542088 1.3812255 2.0672243
## 67 1.5522947 2.8082653 1.2402828 2.2632356
## 68 0.5784840 1.0550336 0.5061475 0.7731667
## 69 2.3136243 4.5958624 2.5278046 2.9065149
## 70 0.8776675 1.4521017 1.0226647 1.5552878
## 71 0.6504724 1.4281425 0.6649097 0.8370323
## 72 1.8666863 3.5690150 1.5968598 2.5979956
## 73 0.3296019 0.5530865 0.3744415 0.5377077
## 74 1.2057956 2.2950261 1.2757906 1.3884323
## 75 1.4994279 3.5215582 1.6083651 1.9424394
## 76 0.7191433 1.3914194 0.7835066 0.9659389
## 77 1.9550954 4.5736800 1.6402818 2.7171445
## 78 1.5275436 2.7198831 1.3039012 1.9964232
## 79 0.7756627 1.4616050 0.8345385 1.1215818
## 80 1.5289954 2.3946764 1.9235684 2.4868926
## 81 2.0290760 3.3541404 2.0108804 2.1091693
## 82 1.3229966 3.0447824 1.1542026 1.5819328
## 83 0.4404022 0.9477266 0.5513603 0.8954589
## 84 0.4903075 0.9091525 0.5428080 0.6854534
## 85 0.6035119 1.2581621 0.7196532 0.6454102
## 86 1.0810299 1.9450024 1.2125286 1.3419666
## 87 0.6177416 1.3025971 0.5808914 0.7026693
## 88 0.4175015 0.6780209 0.4549001 0.5960717
## 89 0.8621639 1.9606441 0.7312521 1.1487573
## 90 0.6634052 1.3805202 0.9426191 1.3614188
## 91 1.2428109 2.5276403 1.2539032 1.6358245
## 92 0.7063637 1.2981933 0.9537642 1.0415905
## 93 0.9124812 1.8781665 0.8703274 0.8726287
## 94 0.8866613 1.6867142 1.0682839 1.2747603
## 95 1.5215309 3.2598646 2.0230931 3.2227860
## 96 1.0875430 2.5625741 1.2648747 1.7087558
## 97 1.0831163 2.0859884 1.1263770 1.0126274
## 98 1.9017628 4.1883040 1.6619484 2.2217191
## 99 1.1913803 2.7765006 0.9883130 1.6907023
## 100 0.6152760 1.3655367 0.5161768 0.8612618boxplot(results, las=1, main="Comparación estimadores con n=100", col = c("green","yellow","purple","blue"), names = c("Estimador1","Estimador2","Estimador3","Estimador4"))
abline(h=1, col="red") 
apply (results,2,mean)## Estimador1 Estimador2 Estimador3 Estimador4
## 1.131178 2.282932 1.132851 1.503110apply(results,2,var)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.3252261 1.4621414 0.2869945 0.5483490Para un tamaño de muesta n=100, se observa que los mejores resultados se obtienen con el Estimador3. El Estimador3 se puede clasificar como INSESGADO, pues su promedio está más cercano a 1 y es EFICIENTE, ya que es el estimador que tiene la menor varianza.
Para n=1000
x=matrix(data=rexp(1000*4,rate=1), nrow=1000, byrow=TRUE)
x1000=x[1:1000,]
estimador1 <- function(x1000) {
estimador_1 <-((x1000[1]+x1000[2])/6) + ((x1000[3]+x1000[4]) / 3)
}
estimador2 <- function(x1000) {
estimador_2 <-((x1000[1]+(2*(x1000[2]))+(3*x1000[3])+(4*x1000[4]))/5)
}
estimador3 <- function(x1000) {
estimador_3 <-((x1000[1]+x1000[2]+x1000[3]+x1000[4])/4)
}
estimador4 <- function(x1000) {
estimador_4 <-((min(x1000[1],x1000[2],x1000[3],x1000[4]))+(max(x1000[1],x1000[2],x1000[3],x1000[4]))/2)
}
for (i in 1:1000){
est1 <- apply(x1000, 1, estimador1)
est2<-apply(x1000, 1, estimador2)
est3<-apply(x1000, 1, estimador3)
est4<-apply(x1000, 1, estimador4)
results<-data.frame(Estimador1 =est1, Estimador2= est2, Estimador3 = est3, Estimador4 = est4)
}
print(results)## Estimador1 Estimador2 Estimador3 Estimador4
## 1 1.4631812 3.1681642 1.7779328 2.5428753
## 2 2.2965257 5.0086135 2.1196047 2.6650204
## 3 0.6233609 1.2877744 0.5303775 0.6126586
## 4 1.5838075 3.6661366 1.5034331 1.7102862
## 5 0.6781607 1.3876453 0.5168281 0.6131542
## 6 2.5257717 4.9028696 2.1101311 2.7121458
## 7 1.1501336 2.1866962 1.3850669 1.7449443
## 8 2.1822611 4.8511592 2.2514906 2.2871224
## 9 1.2464982 2.4537330 1.6593329 1.6005754
## 10 0.7763501 1.8052376 0.6163473 1.1542111
## 11 0.9148419 2.1658800 1.0904913 1.5468830
## 12 0.6273433 1.3280037 0.6012411 0.7395947
## 13 0.9034476 1.7658079 0.9058136 1.0362008
## 14 1.2922098 2.3546696 1.5803731 2.0554893
## 15 1.7660294 3.5445064 1.7775438 2.0758961
## 16 0.9686354 1.9494861 0.8389695 0.9662298
## 17 0.3919468 0.7546404 0.3961693 0.4269493
## 18 0.9083641 1.5265088 1.2036106 1.5936139
## 19 0.4840261 0.8594340 0.7198084 0.7561854
## 20 1.6445924 3.8587874 1.3309696 2.1459601
## 21 1.8374730 4.0238073 1.5224620 2.2976543
## 22 0.8406597 1.5194997 0.6452103 1.2386505
## 23 0.8516837 1.7643581 0.8890698 1.2183992
## 24 1.0964478 1.9700852 0.9555894 1.4830087
## 25 1.1940233 2.3923939 1.0305660 1.3954915
## 26 1.0678769 1.9912797 0.9651459 0.8812704
## 27 0.8554866 1.5045982 1.1676827 1.4568520
## 28 1.1035548 2.2795574 0.9524673 1.1864165
## 29 0.9104449 2.1402418 0.8053032 1.1583955
## 30 1.2193060 2.3200580 1.6554669 1.5470356
## 31 0.5887994 1.0269938 0.7257943 0.9545850
## 32 0.4445841 0.9981362 0.3990131 0.4617963
## 33 1.3827452 2.5465470 1.4844351 1.8881097
## 34 0.3336438 0.6657999 0.3678853 0.4360846
## 35 0.6146407 1.0574313 0.7499467 0.9875731
## 36 1.5849916 2.9143151 1.5633115 1.7907943
## 37 0.8700376 1.9688478 0.9476850 1.1195789
## 38 1.1474860 2.5713824 1.1408660 1.3339407
## 39 0.8034227 1.7455125 0.8395319 0.9796104
## 40 1.7557914 3.8328322 1.9213196 2.8117420
## 41 0.2896163 0.5186780 0.2584365 0.2965779
## 42 1.0498497 2.2737213 0.9221806 1.4948188
## 43 0.8463819 1.6387054 0.8570476 1.2117371
## 44 1.3269820 2.6101933 1.0887077 1.3725050
## 45 1.4068352 2.6782465 1.3163476 1.7546687
## 46 1.4871748 3.3581772 1.2513389 2.2062749
## 47 0.2558678 0.5682135 0.2076656 0.3246227
## 48 1.0183169 1.6657937 1.3442329 2.0508891
## 49 1.0326686 2.3041965 0.9205363 1.4574075
## 50 1.5632460 2.7456893 1.3829563 2.0143805
## 51 1.3823232 3.1718337 1.2195709 1.4339655
## 52 1.1923796 2.3775098 1.3652148 1.2403953
## 53 1.4967116 2.6126528 1.7468202 2.7986181
## 54 1.1816274 2.3074124 1.5001024 1.3533266
## 55 1.6548131 3.5037113 1.5903319 2.2099740
## 56 0.9170729 1.9170646 0.8988650 1.2059349
## 57 1.4075388 2.5987306 1.6489339 1.4131100
## 58 0.8097983 1.7267920 0.6442280 0.8064426
## 59 1.4087855 2.8222514 1.4890600 2.0574645
## 60 0.6842805 1.4368325 0.7881091 0.8952897
## 61 1.4484831 3.0495026 1.2316970 1.6413925
## 62 1.0544128 1.7019758 1.1310370 1.3749913
## 63 0.5934770 1.3603201 0.4731881 0.8290406
## 64 0.6106555 1.0460931 0.6675109 0.6567070
## 65 0.7930971 1.7611216 0.7512318 0.8099892
## 66 1.8032585 4.2087770 1.5104878 2.4962895
## 67 1.3481500 2.6911529 1.1418892 1.2151593
## 68 1.1608892 2.4094793 1.6634784 2.3410366
## 69 0.7807095 1.4418053 0.7022672 1.0540654
## 70 0.8373704 1.7972122 0.8901578 1.0600583
## 71 0.2831697 0.6621370 0.2249445 0.4176091
## 72 0.3648747 0.6219335 0.3506148 0.3440440
## 73 1.2559249 2.4343951 0.9489907 1.4570346
## 74 0.5346708 1.0167285 0.5487075 0.6350937
## 75 0.6932567 1.4711564 0.6973898 0.7720786
## 76 1.5970528 3.1340750 1.3969599 1.9819446
## 77 0.4704660 0.9283891 0.4324085 0.4410495
## 78 1.0083656 2.0510145 0.7876005 0.8539652
## 79 1.7695981 3.5106929 1.4947707 1.9296777
## 80 0.9646986 1.8199467 0.9682021 0.9899989
## 81 0.9436278 1.3876071 1.1092486 1.5813582
## 82 0.7455248 1.3740129 0.7796873 0.9019087
## 83 1.8286428 3.7408632 2.0388397 2.9684154
## 84 0.4394224 0.8260322 0.4479032 0.4315096
## 85 0.8743752 1.6217616 0.6946861 1.1779326
## 86 0.6511402 1.4202537 0.6659084 0.7431997
## 87 1.6351298 3.1154380 1.6061935 1.9315872
## 88 2.4292681 5.2185581 1.8622265 2.2060472
## 89 1.6667391 3.8022792 2.2153332 4.0525339
## 90 0.4910578 1.0941105 0.4678265 0.6073421
## 91 0.3600955 0.6450805 0.3985884 0.5712512
## 92 0.3477044 0.7051920 0.3863968 0.4966687
## 93 0.4475513 0.9221812 0.6614390 0.9512813
## 94 1.1411274 2.3338983 1.0734623 1.0459778
## 95 1.3505854 2.4154934 1.4463801 1.8075973
## 96 0.5291268 1.1206243 0.5025821 0.4482443
## 97 1.3216232 2.7232866 1.1692400 1.1798855
## 98 1.1163883 2.1767113 1.0585484 1.4393835
## 99 1.1005519 2.3675007 1.0829467 1.1979191
## 100 1.5532748 3.0545105 1.2360925 1.7298870
## 101 0.9765472 1.7850126 0.9814795 1.2440799
## 102 0.9709921 2.2343876 0.8960659 1.1354910
## 103 1.0731759 2.2355321 1.0647325 1.4171978
## 104 1.0232488 2.0781960 0.8486195 0.8098687
## 105 0.5588056 1.0182161 0.4793359 0.7702033
## 106 1.3151148 2.9379598 1.3435410 1.6299810
## 107 1.0840110 2.5282266 0.9049424 1.4743861
## 108 0.8353766 1.5749599 1.0663312 1.1916546
## 109 0.7186932 1.3534995 0.5500720 0.9308784
## 110 1.3887440 3.1106976 1.3853309 1.4279520
## 111 0.5671130 1.0737134 0.5931099 0.5990843
## 112 0.4584393 0.9472939 0.4760277 0.7099665
## 113 0.5791195 1.3620166 0.4963591 0.7384529
## 114 0.9472156 1.7389655 0.9873284 1.0611116
## 115 0.3143883 0.5775689 0.3746205 0.3174549
## 116 0.6301868 1.1742887 0.8239567 0.8675455
## 117 2.0217882 3.7799121 1.6928453 2.5465263
## 118 2.1723315 4.3133215 2.2301534 2.3445370
## 119 1.0468352 2.2813228 1.1884490 1.3918926
## 120 0.8062994 1.4374202 0.7342305 1.0448459
## 121 0.4331813 0.9263533 0.3813583 0.4816543
## 122 1.3354819 2.3696109 1.1659255 1.7580676
## 123 0.4434890 0.9703206 0.5542978 0.9197511
## 124 0.7817578 1.3773941 0.8883038 1.3359181
## 125 0.9112011 1.4647040 1.0961421 1.7430093
## 126 0.9423887 1.9078846 1.0488756 1.0468474
## 127 1.0532702 2.1925600 0.8463547 0.9002167
## 128 0.5603084 1.0735834 0.5238559 0.5099148
## 129 0.2076424 0.3810988 0.2536117 0.3182420
## 130 0.6726208 1.2634330 0.7370987 0.6275451
## 131 0.4416320 0.9611716 0.4093077 0.5581967
## 132 0.5954835 1.0669888 0.5351967 0.6473349
## 133 0.5854445 1.1949279 0.5483907 0.6887931
## 134 0.4817549 0.9113355 0.4868087 0.5776035
## 135 0.9218168 1.6379690 0.9628288 0.9013232
## 136 0.2126599 0.4014957 0.2511296 0.2733560
## 137 2.0536275 4.0856189 1.8105677 2.1319949
## 138 0.1189908 0.1855607 0.1580265 0.2535764
## 139 0.5756289 0.9659457 0.7044699 0.7239471
## 140 0.5908962 1.1726796 0.5609856 0.7887789
## 141 0.9435248 2.1373838 0.9749134 1.1858196
## 142 0.5944302 1.1935927 0.5588924 0.5969032
## 143 0.9736371 2.0214714 1.1317280 1.8024677
## 144 0.9489717 1.7445851 1.0497164 0.9232392
## 145 0.9080574 1.6973530 0.8521233 1.0402666
## 146 1.0184982 2.2821168 0.9537816 1.2359826
## 147 1.2619789 2.5818021 1.1543798 1.1951369
## 148 0.8083190 1.8123651 0.8832499 1.0550960
## 149 0.9550425 2.0818852 1.2248185 2.0952416
## 150 1.0830923 2.1672597 0.8611592 0.9257472
## 151 0.5014552 1.1279259 0.5260170 0.6216838
## 152 0.7870192 1.6983609 0.6384612 0.8489466
## 153 0.6723926 1.5920172 0.6304972 0.7822497
## 154 0.7431992 1.4409241 0.7389586 0.9026171
## 155 0.7088087 1.4567255 0.6297394 0.6499997
## 156 0.8306071 1.7929676 0.8263328 0.9416159
## 157 1.2409726 2.4525594 1.1628559 1.6116418
## 158 0.5597652 1.0534427 0.6868206 0.8474418
## 159 1.1516443 2.5120619 0.9537495 1.4521470
## 160 2.1840691 4.5627428 2.0678807 3.0220863
## 161 0.9506882 1.8234804 1.1807026 1.3061611
## 162 0.8325132 1.6156592 0.8015924 0.7726562
## 163 1.8989953 3.6630495 1.6769674 2.3418680
## 164 1.1131424 2.5547968 1.4271750 2.3902610
## 165 0.7198836 1.3968797 0.8158072 1.0788855
## 166 0.3017930 0.4986205 0.3514939 0.5571733
## 167 0.8028850 1.7651277 0.8464848 1.0431406
## 168 0.7822524 1.4359064 0.8416610 1.0294679
## 169 1.4900994 2.8863290 1.2781975 1.3259808
## 170 0.3109683 0.6086608 0.2451277 0.3053122
## 171 1.2877069 2.1515516 1.4488520 1.9188729
## 172 1.1160794 2.3407747 1.0002254 0.8744072
## 173 0.9838984 1.9660035 1.2556315 1.6106722
## 174 1.2159302 2.3153164 1.3329094 1.9278358
## 175 0.3623761 0.6632342 0.3656971 0.3921186
## 176 1.3935742 3.0962592 1.7888893 3.0784579
## 177 1.1643174 2.3298474 1.2000487 1.4336737
## 178 0.4592976 0.7890038 0.4943594 0.6268763
## 179 0.9533473 1.9289409 0.8654831 1.0352336
## 180 1.0263564 1.6703805 1.1976009 1.7667258
## 181 0.5051611 1.0479189 0.4795317 0.4151644
## 182 0.9142661 1.9792817 0.9059962 0.9685543
## 183 1.1352039 2.3758192 1.0064544 0.8933633
## 184 1.1610862 1.7788942 1.5162603 2.5793168
## 185 0.7451429 1.2219821 0.7593031 0.8116389
## 186 1.8518437 4.0438419 2.0477648 1.8766022
## 187 0.6768065 1.3081232 0.7495206 0.9683191
## 188 1.0435113 2.2053601 1.0438774 1.0922371
## 189 0.8084517 1.7184468 0.9290041 1.4791037
## 190 0.5684006 1.2492662 0.5718735 0.6541101
## 191 1.0945574 2.1875462 1.0452426 1.2537127
## 192 1.3135871 3.0464169 1.1971675 1.6223788
## 193 0.1756602 0.3328303 0.2093575 0.2603173
## 194 0.8168510 1.5542566 0.8188472 1.0811157
## 195 1.0742243 2.1497682 0.9811807 1.0053190
## 196 0.7489223 1.6484150 0.7493247 0.8263549
## 197 0.6131610 1.2126846 0.5833917 0.8051733
## 198 0.2009942 0.3973662 0.2350998 0.3047754
## 199 1.0007689 1.9254479 0.8954716 1.4436154
## 200 1.0960420 2.2374925 1.0432697 1.3475344
## 201 1.5870535 3.3608734 1.2892598 1.6270591
## 202 0.5262251 1.0800817 0.4793958 0.5586578
## 203 3.3875590 6.4085353 3.5913128 5.0919573
## 204 1.6532024 3.3328272 1.3719969 1.5933068
## 205 0.9315731 1.8221199 0.9581089 1.0824702
## 206 0.5759806 0.9750637 0.7324906 1.1031323
## 207 0.7501470 1.6573829 0.7639942 0.8193512
## 208 0.9303667 1.5731518 1.0062734 1.3890630
## 209 0.6001648 1.2441503 0.5765667 0.6183953
## 210 1.3035756 2.6088266 1.1215996 1.3408896
## 211 0.7336246 1.4928138 0.7571755 0.8949736
## 212 1.4754539 3.2911450 1.6456135 2.2963630
## 213 1.1313872 1.9894891 1.3899730 1.9912934
## 214 0.6402306 1.2442013 0.5178389 0.7487310
## 215 1.0198097 2.1859325 0.9688716 1.4021133
## 216 0.7501016 1.2441170 0.8605484 1.1798762
## 217 0.9802441 1.9183576 0.9267109 0.9789175
## 218 0.7183793 1.5205903 0.6972634 0.9696682
## 219 0.6392593 1.3495292 0.6350492 0.7522123
## 220 1.5630972 3.1879065 1.3645791 1.7853217
## 221 1.0227074 2.0548741 0.9196292 1.0019065
## 222 1.3208635 2.8360613 1.3031463 1.4563439
## 223 1.1893894 2.7635002 1.2196748 1.2937391
## 224 1.2492693 2.7445546 1.3281805 1.7982038
## 225 1.0202577 2.3080570 0.8775228 1.1102817
## 226 0.3990847 0.7056754 0.3855901 0.4473152
## 227 1.4838132 2.9054624 1.1796365 1.6521711
## 228 0.9857855 1.9569393 0.9963503 1.1964783
## 229 0.4654556 0.8956996 0.5128524 0.4773400
## 230 0.3566196 0.5378876 0.4852242 0.7963583
## 231 0.9506811 2.0324140 1.0328072 0.8635809
## 232 1.2512755 2.7343150 1.3247864 1.1078468
## 233 0.8811777 1.5605211 0.7514461 1.1517260
## 234 0.3177438 0.6979332 0.3173055 0.3852689
## 235 0.8254160 1.7455910 0.8150639 0.9744953
## 236 0.7196925 1.4039632 0.7024403 0.7809822
## 237 0.8671858 1.8096296 0.8758012 0.9350063
## 238 1.7737668 3.8798161 1.4264022 1.6326549
## 239 0.5247658 1.0885246 0.4932782 0.4411602
## 240 0.9863692 1.6605183 1.1514648 1.7250063
## 241 1.3410105 2.5654738 1.1100080 1.7882768
## 242 1.1662257 2.5606107 1.2125240 1.1172488
## 243 2.4755851 4.4512701 2.0387490 3.4249419
## 244 0.3792543 0.8200887 0.3975951 0.3905081
## 245 1.6005304 3.2972789 1.3262071 1.4211768
## 246 1.6409672 3.6078538 1.4401434 1.8265336
## 247 0.6738734 1.3559586 0.8135020 0.9984133
## 248 0.6545805 1.3240957 0.8481130 1.0040384
## 249 0.2995524 0.6056301 0.3533389 0.4480555
## 250 1.0693584 1.9629012 1.2496772 1.7254217
## 251 0.4353138 0.9212193 0.5326927 0.7796238
## 252 0.8490621 1.5249019 0.7266574 1.1013367
## 253 2.0509473 3.9396017 2.0551203 2.0823663
## 254 0.9401113 1.9067940 0.8766853 1.0659522
## 255 1.8434556 3.6325618 1.4816715 1.8376661
## 256 1.9491848 3.7492323 1.6839849 2.6447689
## 257 0.7368100 1.3996597 0.7915983 1.0372988
## 258 1.2534034 2.3587435 1.0390255 1.5494258
## 259 0.3783078 0.6948442 0.5060954 0.5761318
## 260 1.7932506 3.6750195 1.8605290 2.1246134
## 261 1.2859106 2.5875255 1.3590502 1.5397040
## 262 0.9161615 1.6021656 0.8303817 0.9260765
## 263 1.2455177 2.7966713 1.1116021 1.4240331
## 264 0.4663114 0.8223817 0.5029394 0.5151101
## 265 0.6815924 1.4624628 0.9351543 1.4656302
## 266 0.9852525 1.8012085 0.7930283 1.4409081
## 267 0.7457739 1.4891390 0.7129143 0.6863084
## 268 1.0629255 2.0866811 1.0867377 1.4738643
## 269 0.4940323 1.1383987 0.6462167 1.0141053
## 270 0.2308931 0.4978316 0.2769043 0.4555553
## 271 0.6745974 1.4406295 0.7305674 0.5666029
## 272 1.5410613 3.2808650 1.2945372 1.0793166
## 273 0.8017791 1.4808709 0.8465033 1.0809134
## 274 0.6538201 1.4568600 0.6691139 0.7785942
## 275 2.5679952 4.8849022 2.5640138 2.7976639
## 276 1.3850273 2.9504449 1.1731581 1.4556885
## 277 0.6873975 1.3894514 0.7664696 1.1022886
## 278 1.0741984 2.2713624 0.9874452 1.5508388
## 279 2.7657350 5.7234185 2.2926786 2.5651328
## 280 2.0621839 4.5332704 1.8044474 2.0828151
## 281 1.7769999 3.7483715 1.4795433 1.8827210
## 282 0.4523629 0.9798240 0.5089056 0.7007597
## 283 0.8571567 1.8162099 0.7616720 1.1319849
## 284 2.1046531 4.1816063 2.0355526 2.7768778
## 285 1.2951857 2.5919397 1.3662756 1.5996538
## 286 0.2832993 0.5944078 0.2788258 0.3344050
## 287 0.5198134 1.1234614 0.5819918 0.7039927
## 288 0.9627657 1.8362223 0.9464571 1.2490972
## 289 0.3883960 0.8390515 0.3396492 0.3371939
## 290 1.2338834 2.1215926 1.2851030 1.5900043
## 291 0.3229737 0.6149894 0.3525435 0.5205504
## 292 1.3121402 2.2504948 1.5393931 2.4177807
## 293 0.9668542 1.8558106 1.1341374 1.2753375
## 294 0.7693612 1.5266758 0.6217195 0.7099469
## 295 1.5097636 2.9272023 1.5116484 2.0516542
## 296 1.7107517 3.5366807 1.5332629 2.1211330
## 297 1.1352330 2.5628775 1.0172526 1.4305478
## 298 1.3293881 2.6115996 1.3715649 1.4876537
## 299 1.6565962 3.6938021 1.4196040 2.1514003
## 300 0.6437277 1.1500245 0.6221303 0.6982152
## 301 0.4148779 0.7301195 0.3479851 0.5543193
## 302 0.1904940 0.2443529 0.2731212 0.5186262
## 303 0.6659505 1.3530896 0.6428526 0.7299777
## 304 1.0217707 1.9783755 0.8332598 1.3059396
## 305 0.4864364 0.9192526 0.5822910 0.6743853
## 306 1.0634382 2.0855902 1.0102740 1.2710886
## 307 0.6675399 1.4313894 0.6105435 0.8339045
## 308 0.5216247 0.9762791 0.4421505 0.5395365
## 309 0.7159512 1.5350090 0.8413196 1.4413235
## 310 0.4675124 0.9851081 0.5564703 0.7803983
## 311 0.9105340 1.9858953 0.8076657 1.2151752
## 312 0.2463960 0.5342728 0.3143365 0.5005851
## 313 1.0015932 1.9715892 1.1567437 1.5695994
## 314 1.4711409 2.6516625 1.5447055 1.8883231
## 315 0.3481478 0.6964227 0.4290185 0.5367223
## 316 0.6282268 1.3551009 0.8490692 1.3197043
## 317 2.0798916 4.2995800 2.1980971 2.5985300
## 318 0.5176598 1.0436746 0.4227226 0.4127568
## 319 0.4189919 0.7876652 0.4313543 0.4756241
## 320 0.3860900 0.7159141 0.3111921 0.5491016
## 321 0.4773411 0.9008806 0.5031530 0.6209883
## 322 1.1126855 2.3402902 1.0538934 1.3009758
## 323 0.2675356 0.5546367 0.2652140 0.2871840
## 324 1.4190061 2.7638170 1.1999050 1.7838914
## 325 0.6081211 1.3548408 0.8493434 1.4881652
## 326 0.3508894 0.7945897 0.3818890 0.5337724
## 327 0.1423200 0.2677417 0.1618620 0.2161258
## 328 1.3116037 2.4215010 1.3750182 1.4893558
## 329 0.4574991 0.9602184 0.4319992 0.4129194
## 330 0.3266271 0.6522671 0.4211975 0.4425080
## 331 0.5484955 1.1022474 0.7291169 0.7595155
## 332 0.9888503 1.8179455 0.9912801 1.1765058
## 333 1.2506529 2.7081841 1.4398884 1.4782072
## 334 1.2975515 2.7077662 1.1592724 1.4015036
## 335 1.5809677 2.7049953 1.5042563 1.7882166
## 336 0.9510162 2.1064766 1.1988705 1.6904586
## 337 0.9574406 2.0006326 1.0219218 1.0391861
## 338 1.1126658 2.5180246 0.9963690 1.4961898
## 339 1.3205900 2.9175401 1.2283303 1.5675548
## 340 0.3903619 0.8771209 0.5018845 0.7602036
## 341 1.6543603 3.2179981 1.6893224 2.3877533
## 342 0.4580308 0.9233233 0.5422373 0.7454432
## 343 1.2803460 2.6448737 1.0495813 1.1092825
## 344 0.8733192 1.7930457 0.8347232 1.0909085
## 345 0.7450251 1.3823218 0.8134867 0.9765311
## 346 0.6516962 1.3232034 0.8195576 1.0975371
## 347 1.0911387 2.1163722 1.1014683 1.3582946
## 348 1.7110275 3.6276595 1.4185413 1.2572679
## 349 1.2887909 2.6755223 1.0967319 1.1184487
## 350 2.1846887 4.4040573 2.2532780 2.3755216
## 351 0.7084685 1.4807880 0.6257608 0.7086133
## 352 1.4455789 2.7754774 1.3693985 1.7288114
## 353 0.7391370 1.6172051 0.8216697 1.1467393
## 354 1.1642497 2.0493523 1.0798690 1.4442016
## 355 1.7507330 3.2818283 1.5624528 2.3280001
## 356 0.6892583 1.4454787 0.5786666 0.6577006
## 357 0.6499688 1.3802972 0.7735350 0.9168774
## 358 0.5850756 1.0304245 0.5653287 0.7006723
## 359 0.7209599 1.2198281 0.7986297 0.7851167
## 360 0.8412863 1.5289805 0.7714384 1.0948482
## 361 0.7047063 1.4955702 0.6135833 0.8317985
## 362 1.1103672 2.2119342 1.0526732 1.2808723
## 363 1.0734163 2.0555233 1.1172132 1.4205224
## 364 2.0509268 4.6787337 1.8445874 2.7307778
## 365 1.0828438 2.1597909 1.0884837 1.3819217
## 366 0.6897761 1.3968506 0.8806002 1.1601458
## 367 0.7074205 1.5753204 0.5873781 0.8771705
## 368 2.7069963 6.0916837 2.1993693 3.5121870
## 369 1.1781711 2.7892503 1.0513043 1.4682313
## 370 0.3190174 0.6690911 0.3877096 0.5651219
## 371 1.1031650 2.3267190 0.8613800 0.8072326
## 372 0.9177563 1.9934116 0.8697056 1.2113891
## 373 1.2857864 2.2328344 1.5472574 2.3634630
## 374 1.4076274 3.2061072 1.1000291 1.8279142
## 375 1.0645700 1.9875728 1.4911930 1.6136543
## 376 0.8245061 1.9123856 0.9663416 1.3918370
## 377 1.2504331 2.9269965 1.0924035 1.6071607
## 378 1.4721523 3.1694283 1.7557265 2.7188804
## 379 0.9071923 2.1324592 0.7743822 1.0826261
## 380 1.0986399 2.2673025 0.9487203 1.1796023
## 381 1.4010631 2.9396621 1.1562939 1.2662062
## 382 1.7516241 3.9876955 1.4304127 2.5508124
## 383 0.7706661 1.2047073 0.9635165 1.4923131
## 384 3.1360806 6.0679430 2.6158685 3.7792116
## 385 1.3294609 2.7415712 1.1186401 1.1486044
## 386 0.3378856 0.5112443 0.4460032 0.8067361
## 387 1.0446104 2.2124038 1.0285144 0.9802647
## 388 0.7885142 1.6611984 0.8747122 1.0802465
## 389 0.8441627 1.9150197 1.1533299 2.0746586
## 390 1.2452719 2.5514195 1.4247267 1.9969275
## 391 0.3197281 0.6580446 0.2696997 0.2824457
## 392 0.9384780 1.6561672 1.1053809 1.7280611
## 393 1.8883185 3.4233578 2.1218854 3.2145407
## 394 1.2852396 2.6435968 1.4773766 2.0696158
## 395 0.3404276 0.6940966 0.3815206 0.4661074
## 396 1.0202420 2.3003657 1.3064070 2.1775959
## 397 0.4700689 0.9924956 0.3846281 0.3475693
## 398 0.9457694 1.8778283 0.9423748 1.3087096
## 399 0.6434682 1.2579898 0.6541922 0.9408211
## 400 0.6683398 1.3309545 0.8351594 0.9930015
## 401 0.9469019 1.9027413 0.9088609 1.0121798
## 402 0.9852510 1.6986031 1.2606505 1.8490987
## 403 1.2064742 2.1998129 1.0340537 1.5990021
## 404 0.2977235 0.5633772 0.3007962 0.3330217
## 405 0.7453386 1.2049291 0.8972289 1.1712439
## 406 0.8321916 1.8823056 0.6366619 1.0029603
## 407 0.7184117 1.3799766 0.9441462 1.1042902
## 408 0.7388221 1.3288282 0.7191886 0.7673837
## 409 0.8691955 1.7967948 0.9733158 1.4076362
## 410 1.4433916 2.7925450 1.3632394 2.0774080
## 411 0.3469024 0.7348056 0.3241333 0.3911681
## 412 0.7794545 1.3949235 0.7639320 0.8671565
## 413 0.4964294 0.9090277 0.5603219 0.7076910
## 414 1.2067489 1.8587439 1.3893830 1.9471035
## 415 1.1977528 1.8282735 1.5609824 2.7166754
## 416 0.5939000 1.2041458 0.5373850 0.5907440
## 417 0.6804733 1.3605143 0.5413556 0.6952810
## 418 0.9931215 2.2773792 0.8865426 1.3171947
## 419 0.7698745 1.5060414 0.7805861 0.9732213
## 420 1.8860664 3.6209217 2.1786542 2.4246202
## 421 1.4017714 3.1800824 1.2186934 1.3486227
## 422 1.7090090 3.3224739 1.6660761 2.0289181
## 423 0.6851751 1.0773470 0.8681490 1.2504871
## 424 0.4330783 0.9144707 0.4651400 0.6593257
## 425 0.5634744 1.2158841 0.5318168 0.5008469
## 426 1.1026540 2.2380545 1.4018569 1.9239908
## 427 0.9347769 1.6938681 1.0241489 1.4759642
## 428 1.0129045 1.7606749 0.9893305 1.0750335
## 429 0.8514430 1.5260559 0.9099606 1.2474726
## 430 0.3742251 0.7138893 0.3233279 0.5400578
## 431 0.3448448 0.6861864 0.3795236 0.4393980
## 432 1.6320146 3.2648386 1.4971774 1.7261022
## 433 0.3662296 0.7709110 0.4525556 0.5172522
## 434 0.8634985 1.3078866 1.0695488 1.6444776
## 435 1.0603143 2.3592043 0.9689917 1.3489127
## 436 2.1844404 4.8784074 1.9734199 2.4062205
## 437 0.5713471 1.2474995 0.6840553 1.1086825
## 438 2.0257537 4.3847413 2.2274546 1.6625021
## 439 0.7503158 1.5712658 1.0593612 1.6056848
## 440 2.2041526 4.5038574 2.1318335 2.2997932
## 441 1.6649417 3.3882413 2.1622030 2.9393140
## 442 0.3687075 0.6674327 0.4294092 0.5033280
## 443 0.5419539 1.1883576 0.6221878 0.9377175
## 444 1.3895011 2.3617462 1.4995040 2.0424901
## 445 0.9495409 1.9875413 1.0156673 0.8224778
## 446 0.7596926 1.7014703 0.7066843 0.8814863
## 447 0.7359898 1.3233243 0.9143076 1.2368073
## 448 0.8209388 1.8546123 0.7237248 1.0595400
## 449 1.1723797 2.5214775 1.2374347 1.1626608
## 450 0.7327831 1.3312370 0.6111409 1.0176019
## 451 0.9805775 2.0045915 1.1363263 0.9156181
## 452 1.2277136 2.4982031 1.6382096 2.2854939
## 453 0.4247098 0.9472567 0.4382811 0.5632747
## 454 0.3172882 0.5692364 0.3241429 0.3673381
## 455 2.2583130 4.3170376 1.7961994 2.5691653
## 456 0.1411788 0.2617288 0.1733346 0.2159812
## 457 2.2222015 4.3523800 2.4787320 2.9598720
## 458 1.3534648 2.7776022 1.4333356 1.2142354
## 459 1.3111122 2.4552175 1.3295218 1.4797667
## 460 0.2691169 0.4187154 0.3649486 0.5047954
## 461 1.0129288 1.8064340 1.0783244 1.4239380
## 462 1.8341933 3.3556843 1.8858374 2.5550998
## 463 0.9567925 1.9188518 1.0827041 1.4157043
## 464 0.6204888 1.1514075 0.7075547 0.7891459
## 465 0.4475545 0.8304423 0.4729226 0.4654726
## 466 0.7737564 1.8435207 0.6195579 1.0869487
## 467 0.8784016 1.4876630 0.9306083 1.1883720
## 468 0.2863265 0.4915013 0.2826385 0.2825803
## 469 0.4026928 0.8548256 0.4498509 0.7160872
## 470 0.9238097 1.8994190 0.8855933 1.1507213
## 471 0.2199278 0.4492399 0.2836042 0.3950547
## 472 1.3400991 2.8734831 1.4823240 2.1297239
## 473 0.6656931 1.2418113 0.7583077 0.9353923
## 474 1.0008870 1.9453603 1.0387520 0.9672734
## 475 0.9768371 1.8224814 0.8843147 1.1085782
## 476 0.1488165 0.3009895 0.1810860 0.1673800
## 477 1.2457523 2.5835833 1.1695247 1.0989441
## 478 1.1720179 2.2456549 1.1616373 1.3316625
## 479 0.6138526 1.4403193 0.7525739 1.2039362
## 480 0.4952981 0.9460050 0.5259965 0.7680681
## 481 0.6324247 1.2243419 0.5917913 0.8394772
## 482 0.8007236 1.3464306 0.8055951 0.7915990
## 483 0.9889774 2.1529960 1.0948985 1.5063656
## 484 0.9750823 2.0455429 0.8790150 1.1951791
## 485 0.3787937 0.6496078 0.3409112 0.4682611
## 486 0.8612504 1.6376110 0.7111330 0.9728598
## 487 1.0076401 1.8948683 0.9066849 1.4050271
## 488 1.8753853 4.2521333 1.7552709 2.1961980
## 489 0.6474365 1.2329885 0.5945235 0.8673116
## 490 1.7158486 3.2312744 2.2131396 2.3060182
## 491 1.6482928 3.3318270 1.7009064 1.9488286
## 492 0.7573562 1.6297184 0.7195759 0.7503263
## 493 1.0709031 2.3276238 0.9097518 1.3784581
## 494 0.9190248 1.4013600 1.0509911 1.4914266
## 495 0.6561112 1.1881878 0.6222383 0.5292694
## 496 0.8429237 1.9738777 0.7098603 1.1205168
## 497 1.7008761 3.3327235 1.3762828 2.0723665
## 498 1.5272150 3.2571409 1.2170120 1.5143703
## 499 0.6823359 1.2111657 0.7875907 1.2615811
## 500 1.2159285 2.3599408 1.0339212 1.5250066
## 501 0.7951316 1.3859950 0.7337539 0.9434495
## 502 1.1000754 2.1491627 0.9420709 1.3501250
## 503 1.0200979 1.8865435 1.1310464 1.1779128
## 504 1.2564136 2.8349546 1.0412758 1.7088619
## 505 1.0001574 1.8851388 1.2485969 1.4184810
## 506 1.0760235 1.9046946 1.3538341 1.3436480
## 507 0.3447975 0.6528015 0.4372444 0.4838073
## 508 0.8580869 2.0425969 0.8796302 0.9133389
## 509 1.0479183 2.0419124 1.0906223 1.6155218
## 510 1.6713087 3.3448882 1.5973640 2.1826219
## 511 1.0179196 2.3468794 0.8074427 1.4072216
## 512 0.6443255 1.3771848 0.7714429 1.1935974
## 513 0.6280253 1.2373274 0.8874747 1.0553875
## 514 2.1002323 4.6604300 1.6738231 2.5310253
## 515 0.5210206 1.1558594 0.4999763 0.4804938
## 516 0.8269782 1.5058424 0.8045608 0.9136833
## 517 1.9965540 3.8285821 2.2203860 2.3677473
## 518 0.6097125 1.1364078 0.7066939 0.5961538
## 519 1.5117540 3.2649202 1.1484540 1.3796333
## 520 0.4641443 1.0336644 0.5546800 0.8357499
## 521 0.4892791 0.8899919 0.5898411 0.4979025
## 522 1.9493938 4.1435999 2.4617215 3.7368077
## 523 0.6598807 1.4318433 0.5722878 0.5559942
## 524 0.5007883 1.0407009 0.5743854 0.7427305
## 525 1.1435579 2.1890605 1.2673111 1.3488874
## 526 0.4878892 0.8618684 0.6177234 0.7851327
## 527 0.8150835 1.6147955 0.8138304 0.9365458
## 528 0.9013238 1.7343040 0.8295564 1.2337886
## 529 0.7732301 1.2530192 1.0512136 1.5777228
## 530 1.2603600 2.3341752 1.0398042 1.8723683
## 531 0.9439019 2.1602479 0.9289604 0.9935363
## 532 1.0591913 2.0052891 0.8592872 1.1851043
## 533 0.8209210 1.7807272 0.7816898 0.9726239
## 534 2.7886953 5.3175954 2.3540597 3.6969531
## 535 1.4501517 2.7636015 1.4391912 1.5957245
## 536 0.9483280 1.8329355 1.0344810 1.1982496
## 537 1.4289128 3.0755801 1.1833585 1.4957926
## 538 0.7851171 1.2832804 0.8249202 0.9731262
## 539 2.7662097 4.5909394 3.2248430 4.9695170
## 540 0.5996013 1.0413255 0.7857298 1.0963032
## 541 0.5854744 1.2673369 0.7426809 1.2086933
## 542 0.5024105 1.0587294 0.5179743 0.4870760
## 543 0.4915001 1.0067414 0.4024533 0.4332269
## 544 2.7518601 5.4239376 2.7332405 3.3624613
## 545 0.4834800 0.9120539 0.5669534 0.6390940
## 546 0.8149191 1.9246968 1.1364529 2.1279369
## 547 2.6753936 4.7531053 2.4648009 2.7074779
## 548 2.0703026 4.1606033 1.8687857 2.5697406
## 549 0.4224885 0.7372740 0.4145238 0.4238210
## 550 0.7691165 1.5857937 0.7096671 0.9526050
## 551 0.7522144 1.5660874 0.8711377 1.3634265
## 552 2.4686838 4.4498411 2.4102887 2.3971628
## 553 0.6640646 1.2152877 0.6396259 0.5944728
## 554 1.5152833 3.1190331 1.3992293 1.4858765
## 555 0.7357692 1.5364751 0.7561983 0.7538757
## 556 1.1623135 2.6316805 1.0587586 0.9948344
## 557 0.9309934 1.9430942 0.9663832 1.2766050
## 558 1.6001728 2.8635629 1.3996322 2.0203418
## 559 1.2509404 2.6247090 1.3345898 1.1944078
## 560 0.5311484 1.0361010 0.6275637 0.6647401
## 561 1.4352754 3.1059489 1.2865757 1.9453439
## 562 1.1202918 2.4771990 1.0209933 0.9669456
## 563 0.8117569 1.6622859 0.8949186 0.7412665
## 564 1.8494232 3.7769983 1.6733521 1.8245182
## 565 1.2507288 2.3581843 1.0714046 1.6313227
## 566 1.0447585 2.0348151 1.1988358 1.3736195
## 567 0.5995555 1.4040310 0.5351146 0.6421491
## 568 0.7919173 1.5640098 0.8345729 1.1620857
## 569 0.8157283 1.6658775 0.7509392 0.9598238
## 570 0.7859188 1.6165494 0.8531489 0.7841326
## 571 0.9905889 1.9592667 0.9470092 0.9820651
## 572 0.6597251 1.3373598 0.8074720 1.1166585
## 573 0.4371852 0.9074778 0.5439067 0.7555728
## 574 0.9048273 1.8143366 0.9584287 1.3110258
## 575 1.0094109 2.0340396 1.2005568 1.6879527
## 576 0.7964873 1.5773329 1.0160231 1.2850999
## 577 0.4522331 1.0135571 0.3932545 0.5564932
## 578 0.5820013 1.2481832 0.6226769 0.7074989
## 579 1.1928056 2.7359451 1.0085395 1.6618430
## 580 1.3462302 2.6950394 1.1743279 1.4708934
## 581 0.4981426 1.0058979 0.4452914 0.5216501
## 582 0.4471947 0.8867522 0.5487931 0.7443151
## 583 2.1192946 4.1256124 2.2539837 2.4155630
## 584 2.0989635 3.9447295 1.9402562 2.0011193
## 585 0.7571337 1.4954750 0.7568497 0.8704072
## 586 0.4007402 0.8275854 0.5027452 0.5223888
## 587 0.7444694 1.4186365 1.0205087 1.0833225
## 588 1.9781534 3.5284516 1.8559660 1.9463278
## 589 1.7388374 3.9105748 1.4770013 2.4890561
## 590 2.1212936 4.6093323 1.8753722 3.0092141
## 591 1.3243888 2.8047076 1.2124099 1.4330838
## 592 0.4864252 0.9513735 0.4356878 0.3457288
## 593 0.7990913 1.5614806 0.9168608 0.9071377
## 594 1.2581600 2.5366185 1.1286191 1.2691823
## 595 0.4649023 0.9838345 0.3636378 0.3750047
## 596 1.3138669 2.5038629 1.0907158 1.3576307
## 597 1.9613625 4.3441336 1.6914737 2.8497714
## 598 0.3910909 0.7037845 0.3326001 0.4519308
## 599 1.3687863 2.5458977 1.5099337 2.0284175
## 600 1.6269733 2.9546602 1.7125055 2.1195400
## 601 0.8200541 1.8006877 1.0225013 1.3541747
## 602 1.4871781 2.7062427 1.6021880 2.3498287
## 603 0.7885240 1.5386858 0.7151477 0.8906070
## 604 0.7557705 1.5035952 0.7757070 0.8635847
## 605 1.1540785 2.1744011 1.0371957 1.0227126
## 606 0.5796337 1.0307758 0.6106114 0.8028552
## 607 0.9548838 2.1848362 1.2220401 2.1282328
## 608 0.2191662 0.4722349 0.2328433 0.3153484
## 609 3.0093175 6.9769770 2.4949680 3.7430204
## 610 0.6653366 1.2645547 0.5824990 0.8533466
## 611 1.2854964 2.7079422 1.2111672 1.7658530
## 612 0.3346642 0.6934052 0.2938743 0.3963196
## 613 0.4491423 0.7669977 0.4862354 0.6714127
## 614 1.3142081 2.5535211 1.3037838 1.7435548
## 615 0.6421747 1.1451671 0.5855949 0.8346558
## 616 0.3085012 0.5467377 0.3706148 0.4952242
## 617 0.5930670 1.3618080 0.7187381 0.9644858
## 618 1.1649746 2.3227514 1.0362821 0.9107134
## 619 0.7463426 1.3515001 0.6982055 0.9360944
## 620 0.8588119 1.9681227 0.7257363 1.1567089
## 621 0.5496765 0.9442613 0.6486990 1.0558691
## 622 0.3444741 0.6201454 0.3109576 0.4606525
## 623 0.7710965 1.6503894 0.6727393 0.6897175
## 624 1.0565886 2.2079385 1.0179990 1.2238877
## 625 0.8631624 1.8699669 0.8512445 0.9566048
## 626 1.0563264 2.0839994 1.2080946 1.4075579
## 627 1.3221161 2.4102567 1.1739448 1.6750512
## 628 0.7509648 1.3384532 0.7763054 0.8026854
## 629 0.6800757 1.3019189 0.8982213 1.0173315
## 630 1.7156066 3.3948635 1.6374228 2.1936332
## 631 0.3832607 0.8116684 0.3093645 0.3638981
## 632 1.0946457 2.0874576 1.0005695 1.3348481
## 633 0.7114659 1.3516048 0.6019399 0.9941610
## 634 2.5658083 4.9485712 2.3212872 3.6190402
## 635 1.3920095 2.6068134 1.2787677 1.7888968
## 636 1.4959436 3.0177132 1.3434285 1.4706336
## 637 0.2641106 0.4612304 0.3685229 0.4495492
## 638 0.2993884 0.6852796 0.2565475 0.3564284
## 639 0.7426979 1.1945903 0.9377132 1.3504748
## 640 2.2747406 5.3321097 1.9193818 3.1443483
## 641 0.7225351 1.3939727 0.6708822 0.5285030
## 642 1.3225354 2.5129395 1.2177578 1.7882939
## 643 0.8759641 1.8944055 0.8947234 1.0054004
## 644 1.2330089 2.6737805 1.2671410 1.5103388
## 645 1.0878048 2.4747270 0.9078231 1.5030497
## 646 2.7230093 4.3976291 3.0571467 4.3581241
## 647 0.4724045 0.8152617 0.5048377 0.7056800
## 648 0.8924297 1.5403195 1.0423601 1.6245019
## 649 0.5432931 0.9932536 0.6096922 0.8631996
## 650 0.6593794 1.2590973 0.5562901 0.8679254
## 651 0.7779586 1.2983800 0.8392964 1.0965669
## 652 0.8529575 1.8706533 0.9899352 1.4651713
## 653 1.3224349 2.4488007 1.0409142 1.7805038
## 654 0.7109074 1.5102248 0.5666664 0.5871832
## 655 0.7609188 1.6230053 0.7352451 0.8823524
## 656 1.2725444 2.4416547 1.4235779 1.7070825
## 657 1.7508842 3.6838600 1.5753919 1.3007130
## 658 0.4644268 1.0504489 0.4740130 0.5687206
## 659 0.7448979 1.4945973 0.6594927 0.8157987
## 660 0.5681492 0.8700865 0.7183784 1.1028176
## 661 2.3322005 4.3829805 2.0636403 3.0239005
## 662 0.3992023 0.6960242 0.4952042 0.6294478
## 663 0.9287417 1.7761673 1.0334321 1.1551415
## 664 0.5154965 0.8234718 0.6876773 0.9430918
## 665 1.8406207 3.9567114 1.5842577 2.3611188
## 666 1.7388466 3.7793239 1.5840103 1.5808462
## 667 1.4412237 3.3323991 1.3681352 1.5806632
## 668 1.7317203 3.3716661 1.4529781 2.0618942
## 669 1.1088241 2.0541417 0.9293429 1.6320063
## 670 0.7094325 1.2910608 0.8163120 0.7003887
## 671 0.5951278 1.1026090 0.6819149 0.9951232
## 672 0.9317322 1.7642558 0.9162138 1.0374169
## 673 0.7967096 1.5422906 0.8622216 1.2445829
## 674 0.3462349 0.7612810 0.3088974 0.4893408
## 675 1.8160761 3.3707214 1.8079525 2.3754307
## 676 0.5222147 0.9382737 0.5083272 0.6193578
## 677 0.4208675 0.8492307 0.3702763 0.4775419
## 678 1.8475160 4.0783214 2.0404975 2.9651168
## 679 0.3783969 0.8276106 0.3648002 0.5033712
## 680 0.4674697 0.9279360 0.4710989 0.6448794
## 681 1.3610952 2.6063162 1.1424150 1.7458286
## 682 0.7602659 1.6036048 0.9387502 1.2367937
## 683 0.2915362 0.6014881 0.2401041 0.2428968
## 684 2.8660325 6.3475850 2.2698039 3.4275632
## 685 1.4881153 2.8591082 1.6312375 2.0316663
## 686 1.3295020 2.7469318 1.5397117 2.1922719
## 687 0.8952051 2.0098732 0.7800067 1.2412214
## 688 1.2803553 2.2002599 1.1554936 1.5614914
## 689 1.6993995 3.4807906 1.3392613 1.3733332
## 690 0.6711320 1.1362935 0.6590541 0.6846680
## 691 0.9171900 1.8440305 0.8973955 1.2768783
## 692 0.6259456 1.3973346 0.7578990 1.2656042
## 693 1.2452356 2.1498231 1.5406737 2.1451416
## 694 1.2651168 2.4440766 1.0743310 1.4472668
## 695 1.0162560 2.1499021 1.0750455 1.4408271
## 696 0.3040252 0.5480721 0.3504765 0.4260708
## 697 1.7163220 3.6844719 1.5651467 2.4276972
## 698 0.7947378 1.6265650 0.7540769 1.0101326
## 699 1.5006401 3.2011061 1.2130633 1.5445151
## 700 0.6338373 1.4465815 0.8215898 1.4755298
## 701 0.5294181 1.1524417 0.6050906 0.9471062
## 702 0.7378141 1.3314196 0.8573811 0.7105969
## 703 1.3215957 2.5139773 1.0439635 1.4389474
## 704 1.5397972 3.2516440 1.8373365 2.4197834
## 705 0.1886470 0.3891236 0.2384032 0.3226179
## 706 0.5642951 1.0768148 0.5346574 0.6097110
## 707 1.3319270 2.4526156 1.3171886 1.4674513
## 708 1.6056119 3.7826016 1.2397016 2.2933948
## 709 1.2866697 2.3363990 1.3315887 1.5333760
## 710 0.4129418 0.8545220 0.3292780 0.3554290
## 711 0.4966616 0.9006020 0.7205284 0.7452622
## 712 0.6982580 1.5378112 0.8090278 1.2267617
## 713 0.3966582 0.7391751 0.3466809 0.5741418
## 714 0.5940109 1.1453887 0.5656511 0.8520383
## 715 1.0426367 2.3435222 1.1403543 1.5448613
## 716 0.9444409 1.7307361 1.0308897 1.4811009
## 717 0.7468353 1.5008369 0.6109572 0.7859588
## 718 1.5007628 3.2954470 1.6623085 2.4079278
## 719 1.0151721 1.9164510 1.1779365 1.3289399
## 720 1.0904528 1.7854583 1.2213805 1.3293100
## 721 0.7768616 1.3101588 0.8713383 1.2403867
## 722 1.3830650 3.0300400 1.1525903 1.6542149
## 723 0.7665082 1.3656299 0.6388547 1.0306205
## 724 1.5663578 3.4591905 1.3686430 2.3236603
## 725 1.5839089 3.7185490 1.2398376 2.3238291
## 726 0.4594621 0.8672938 0.4731423 0.6632051
## 727 1.0426259 1.3837234 1.4970160 2.8499501
## 728 2.4949791 4.5273905 2.2075094 3.0794577
## 729 1.4245808 2.9994052 1.4205907 1.7116380
## 730 0.3715835 0.7214522 0.3490421 0.4493857
## 731 0.5282915 0.8553083 0.6649017 0.9135251
## 732 0.6834656 1.3783020 0.6568804 0.8873995
## 733 1.2626196 1.8837251 1.5596950 2.5713438
## 734 0.4464541 0.8716628 0.5422616 0.5277060
## 735 1.1710551 1.9635399 1.2262774 1.5044272
## 736 3.0206972 6.1924965 3.0465887 3.8502015
## 737 1.2221610 2.6673879 1.1015215 1.4707255
## 738 0.6739131 1.3615660 0.5845044 0.7498726
## 739 0.7368078 1.2852750 0.6918901 0.8791764
## 740 0.8710312 1.8537099 1.1914808 1.6490109
## 741 0.9845173 1.7158001 1.0330275 0.8930806
## 742 0.3729443 0.8213862 0.3751183 0.4082363
## 743 0.5471288 1.1783057 0.5915468 0.7831781
## 744 0.2930788 0.6150194 0.2788093 0.3703549
## 745 0.4511247 1.0460506 0.6274704 1.1741631
## 746 1.0867701 2.0949247 0.9545914 1.5175244
## 747 0.9117679 1.9273563 0.6934289 0.7044118
## 748 0.8170721 1.4665562 0.7517954 0.7119066
## 749 1.2178105 2.5935342 1.0176386 1.2403132
## 750 0.9891444 1.6886322 0.8684621 1.2359077
## 751 0.2842574 0.5869389 0.3254820 0.3699363
## 752 1.5682388 3.2508017 1.5081930 1.7167009
## 753 0.1154666 0.2093257 0.1511367 0.1819515
## 754 0.5389018 1.0528721 0.4294521 0.5061214
## 755 0.8029849 1.7408472 0.6690338 0.9538099
## 756 2.3176894 5.0945932 2.1299673 2.9925074
## 757 2.6548113 5.1375794 2.5686440 3.4053883
## 758 0.6266607 1.1273138 0.5839560 0.4873999
## 759 1.8204981 4.1754250 1.4587001 2.5957037
## 760 0.8551680 1.3804008 1.1248140 1.7112854
## 761 0.6504760 0.9937500 0.8665933 1.4829797
## 762 1.4120152 2.8286774 1.4307592 2.0510606
## 763 0.3718631 0.7414879 0.4102458 0.3963060
## 764 0.8287574 1.6083066 0.9925963 1.1091118
## 765 0.6422585 1.4315044 0.7539851 1.1981745
## 766 1.8491193 3.7376290 1.7419296 2.2333282
## 767 0.3690030 0.8243484 0.3169496 0.3425102
## 768 1.0332531 1.7302655 1.0065811 1.0074156
## 769 1.8698105 3.8665892 1.7931410 1.6626836
## 770 0.3144401 0.6624428 0.3008351 0.3270490
## 771 1.2268711 2.4964901 1.1716889 1.1367210
## 772 1.8549330 4.0846045 1.5028784 1.7698090
## 773 0.7329918 1.3713930 0.6012645 0.8198870
## 774 0.5753299 0.9507639 0.6497098 0.9272717
## 775 1.3370085 2.9166608 1.1429457 1.5930392
## 776 0.4672523 1.0686226 0.4703967 0.5262306
## 777 0.8319214 1.5297432 1.0213278 1.1353436
## 778 0.1760986 0.3435439 0.2054110 0.2218765
## 779 1.1118918 1.9887728 1.2285496 1.7899982
## 780 0.6555484 1.3467712 0.7298695 0.7204048
## 781 1.5078349 2.7126324 1.6548887 2.3705184
## 782 0.8896953 1.9115254 1.0164707 1.5765155
## 783 1.6787267 3.3750474 1.4510695 1.6706314
## 784 0.7233093 1.5309107 0.8317359 1.2900006
## 785 0.8473912 1.6305543 0.8589690 0.9696786
## 786 1.5736815 3.1386881 1.4294164 1.7040951
## 787 0.3922152 0.6662819 0.4338509 0.4878631
## 788 1.0624974 1.8487070 1.0095080 1.2333875
## 789 0.3813277 0.5825203 0.4948699 0.8383676
## 790 1.2829055 2.7711291 1.0269677 1.0335175
## 791 0.6360267 1.3489245 0.7517125 1.0673970
## 792 0.4176445 0.7174529 0.5942348 0.7241246
## 793 0.7132741 1.1316172 0.9505002 1.4974299
## 794 2.1302633 4.2308710 1.8658367 2.5048268
## 795 2.2038221 4.6986565 1.9054686 2.3718270
## 796 0.6941029 1.4733715 0.7459448 0.9952135
## 797 1.0358884 2.1716674 1.1033941 1.5700837
## 798 0.7286249 1.4691940 0.5824191 0.7119178
## 799 0.8509895 1.7609529 0.7712737 0.7443726
## 800 1.1607579 2.2065827 0.9487588 1.5650898
## 801 0.7197629 1.4961259 0.6673747 0.7343752
## 802 0.5464476 0.9199840 0.6209138 0.8348663
## 803 0.8108695 1.5748858 0.7437758 1.0633298
## 804 1.5700227 3.2615896 1.5293516 1.7805991
## 805 1.2344840 2.5274049 0.9556171 1.0968852
## 806 0.1952930 0.3319954 0.2246643 0.3642688
## 807 0.7441652 1.7483204 0.6287677 0.9765807
## 808 1.0766773 1.8397648 1.3108814 1.5829967
## 809 0.4789684 0.9317472 0.4954185 0.6504461
## 810 2.4780371 5.3130583 2.4391957 3.0604874
## 811 0.8501414 1.6399200 0.7229962 0.7061114
## 812 0.5813783 1.2740130 0.4487130 0.6151462
## 813 0.9314344 2.0745458 1.1588161 1.9419265
## 814 1.4111108 2.4583019 1.3302263 1.6720730
## 815 1.5165332 3.1712637 1.3567595 1.2489048
## 816 0.6953299 1.2241531 0.7093948 0.7859751
## 817 1.2340907 2.1919189 1.2527400 1.2110411
## 818 0.4895137 0.6363203 0.7193432 1.3500404
## 819 0.8384567 1.5889783 0.6912777 1.0885992
## 820 1.2414471 2.8798549 1.1622424 1.4446708
## 821 1.4400568 2.6576448 1.4614302 1.5654606
## 822 1.2558299 2.3027679 1.3829195 2.0522932
## 823 1.1440702 2.3374122 1.4400614 1.6531061
## 824 1.8613148 4.2313419 1.4485188 2.3827468
## 825 0.9749711 1.7827630 1.0425067 1.2815830
## 826 0.4121620 0.8364270 0.4809471 0.6837505
## 827 0.9966395 1.8961649 1.4189923 1.6623912
## 828 2.2823696 4.4995868 1.9321320 2.6418173
## 829 0.4387532 0.8345713 0.4300882 0.6103366
## 830 1.1948444 2.5354658 1.1715925 1.6529036
## 831 0.9949123 2.2934268 1.0673412 1.2982988
## 832 1.8919347 4.3142244 1.5572330 2.5786930
## 833 0.8584446 1.8465186 0.8938070 1.1473593
## 834 0.6408938 1.1334420 0.6566966 0.6352836
## 835 2.0155499 4.3737439 2.2883586 3.1495851
## 836 1.5608962 2.6089186 1.6281015 1.7066945
## 837 0.7829910 1.5573323 0.7610014 0.7379370
## 838 1.3324142 2.7526504 1.4043770 1.9769933
## 839 1.1749908 2.4643704 1.0275954 1.0100834
## 840 1.3052692 2.0436033 1.5711597 2.3697322
## 841 1.1003524 2.1206811 0.8481308 1.3227436
## 842 0.8927883 1.6771900 0.9006678 1.1275599
## 843 0.5600217 1.1615552 0.5474662 0.7750209
## 844 0.2975729 0.5444301 0.2980984 0.3175347
## 845 1.2243346 2.4824019 1.0634722 1.3803793
## 846 0.5692327 1.0726870 0.4689157 0.5757096
## 847 1.7841522 3.1010452 1.9644721 2.7447297
## 848 0.4733163 0.9220430 0.4459084 0.4280061
## 849 0.7148774 1.4179548 0.8480784 0.8098281
## 850 1.1842099 2.1636592 1.0188146 1.4669891
## 851 1.1941711 2.1906831 1.0602595 1.4913186
## 852 1.0342059 2.2555275 1.3817864 2.3128497
## 853 0.6179532 1.3676978 0.5703302 0.8266387
## 854 0.7307487 1.2890512 0.7717595 1.0269133
## 855 1.2153539 2.1883375 1.6209124 1.7601285
## 856 0.9107522 1.5066695 1.0076135 1.3251404
## 857 0.3417530 0.5821706 0.4194038 0.6457497
## 858 0.6073551 1.0254398 0.7198494 0.7747289
## 859 0.4232162 0.7467533 0.5165650 0.6159615
## 860 0.6180343 1.3643643 0.6557714 0.8233299
## 861 1.4408733 3.2647479 1.4457226 1.5034087
## 862 0.8936468 1.4104975 1.0729553 1.3218052
## 863 0.9229936 1.7638804 0.9102598 1.1493834
## 864 1.1534723 2.6333427 1.2893092 1.7534855
## 865 1.0981571 1.7695538 1.1678339 1.4506633
## 866 0.8667577 1.9270235 0.8404299 0.9489890
## 867 0.8381536 1.9393699 0.6770857 1.1009015
## 868 0.2406365 0.4500605 0.2941335 0.3342241
## 869 0.9521390 1.8061631 0.7960003 0.9120849
## 870 0.6158891 1.1969825 0.5501659 0.8308910
## 871 1.1785024 2.4895661 0.9373182 1.0364594
## 872 1.2556397 2.3672397 1.2404408 1.4364946
## 873 0.8404018 1.9357110 0.8282348 0.9083094
## 874 1.7345446 3.3612853 1.5690839 1.7370340
## 875 1.7781194 3.7208952 1.7320442 1.7774634
## 876 1.0045641 2.0423134 1.1335794 1.5538632
## 877 0.7300596 1.0601566 1.0397234 1.7320363
## 878 1.6927267 3.1741887 1.3736042 2.3034070
## 879 0.9871905 1.7137496 0.9367410 1.1667504
## 880 1.0500984 2.4368463 0.9039614 1.1966570
## 881 1.0794379 2.3798903 1.3090424 1.4978992
## 882 1.6226695 3.4755204 1.7173509 2.2475580
## 883 0.8867904 1.9776302 0.9601027 1.1975342
## 884 1.2271919 2.2856929 1.2274090 1.5830204
## 885 1.4011224 3.2409186 1.1908330 1.8332846
## 886 1.5565308 3.2648744 1.4732909 2.2919586
## 887 0.8657563 1.9854368 0.8028565 1.0589668
## 888 0.8799809 1.9335952 0.7986092 1.2293398
## 889 0.8664402 2.0040085 1.0844517 1.8204804
## 890 1.7345452 4.0064703 2.4461589 4.4257239
## 891 0.7039971 1.1561868 0.7901055 1.0566705
## 892 0.3289808 0.6374630 0.3665943 0.3800293
## 893 0.1510932 0.3428602 0.1976044 0.3517815
## 894 2.2127670 4.2527713 2.0122742 2.9602073
## 895 1.4115644 3.0457590 1.4776941 1.8964787
## 896 0.2939591 0.6274187 0.3055957 0.3063549
## 897 0.1847922 0.3683771 0.1844569 0.2121026
## 898 1.0766459 1.9512817 0.9015777 1.3927773
## 899 0.9169124 1.7340987 0.8103244 1.1782586
## 900 0.2251962 0.4370318 0.2293790 0.2665959
## 901 2.0077140 4.4849476 1.9792366 2.0328590
## 902 1.2276273 2.1675329 1.1416649 1.2734907
## 903 1.2334601 2.4599986 1.1636553 1.4064966
## 904 1.2212715 2.1956098 0.9515975 1.7817415
## 905 0.3716371 0.7877760 0.3230977 0.3097479
## 906 0.3887062 0.6632264 0.4049398 0.4879804
## 907 0.3880718 0.7518210 0.5382507 0.5437078
## 908 1.4568143 2.9909553 1.5071251 1.7913566
## 909 1.6197826 3.6485404 1.5744094 1.9297422
## 910 0.7881182 1.7015411 0.7737850 1.0495336
## 911 0.8921201 1.6810276 0.7982830 0.9515139
## 912 0.8791068 1.9468630 0.8146569 1.2103467
## 913 0.4960920 0.7460456 0.6257239 1.0570022
## 914 0.3851030 0.8067791 0.3933114 0.4341826
## 915 0.7516314 1.4501068 0.7476958 0.8279029
## 916 1.0929726 2.5039651 0.9221469 1.5162155
## 917 0.8472784 1.9569085 0.8558842 0.8710158
## 918 0.6720345 1.3391055 0.6362775 0.7613582
## 919 0.4875841 0.7083143 0.6267700 1.0893680
## 920 0.5134113 1.0095823 0.6072728 0.7621811
## 921 0.8647325 1.8047117 0.8678699 1.1657302
## 922 0.7966062 1.4098632 0.7800920 0.9086216
## 923 1.0158758 1.8358416 1.0291156 1.3431109
## 924 0.6947562 1.2732866 0.8019844 1.1103692
## 925 1.6844314 3.4499066 1.6369655 2.3501213
## 926 0.3678961 0.7710909 0.3435536 0.4211689
## 927 0.3078743 0.5218198 0.3743978 0.3751525
## 928 1.2301122 2.8264752 1.3144497 1.6133299
## 929 1.5038921 2.7862932 1.2801073 2.2017800
## 930 0.7688038 1.3060179 0.9807751 1.3679719
## 931 1.2033252 2.4239418 0.9843432 1.1797731
## 932 1.2552496 2.3050757 1.3844657 1.9442536
## 933 0.5979069 1.1224806 0.4929590 0.8101618
## 934 1.5953780 3.0064118 1.6437274 1.7985425
## 935 1.9677032 4.4196418 1.6396244 2.5359187
## 936 0.6711704 1.3818644 0.5575239 0.5499143
## 937 0.6530207 1.3557827 0.6545780 0.7025188
## 938 1.0236654 1.9822418 0.8689488 0.9802629
## 939 0.9221856 2.0432359 0.9304801 0.9503135
## 940 1.6515301 3.1765459 2.0351465 2.4307747
## 941 0.5547560 0.9997929 0.5920876 0.8307680
## 942 0.3014815 0.5834921 0.2587368 0.2745038
## 943 1.2994149 2.3683308 1.6930886 1.9090581
## 944 1.0983939 2.1436950 1.1045511 1.3551264
## 945 0.9301433 2.0533706 0.8094665 0.9802772
## 946 0.3751827 0.6742320 0.3721206 0.4356656
## 947 0.1072729 0.2365069 0.1082040 0.1062341
## 948 0.5151279 0.9021090 0.4946506 0.5565553
## 949 0.8495874 1.5043954 1.0131093 1.2732024
## 950 0.5443162 1.0929276 0.4330117 0.4911303
## 951 0.2593044 0.5009282 0.2966398 0.3288506
## 952 0.5889680 1.1446815 0.5109655 0.7089959
## 953 0.9879530 1.9883666 0.9555003 1.0703707
## 954 0.5874607 1.0519730 0.5972428 0.6704819
## 955 0.7439384 1.3585232 0.8539391 0.7238975
## 956 0.7560077 1.7445925 0.6592488 0.9521444
## 957 1.1312515 2.3859889 1.0182445 1.2879333
## 958 0.5927712 0.9672854 0.6640280 0.9635709
## 959 0.3451558 0.7097825 0.3263705 0.4180605
## 960 2.6643401 5.1470188 2.2106430 2.6463994
## 961 1.1052057 2.3750854 0.8960861 0.8450528
## 962 0.6621958 1.4976744 0.5679006 0.9440493
## 963 1.0087288 1.9126135 0.7998606 1.1226405
## 964 0.7741248 1.8133058 0.7337022 0.8578185
## 965 1.9898015 3.9296776 2.2373087 2.4557716
## 966 0.6642519 1.4141243 0.7866611 1.2495471
## 967 0.9412902 1.7794822 1.0992206 1.0683596
## 968 1.0880422 2.2610754 1.2180854 1.7032757
## 969 1.4288740 2.6049694 1.6568531 2.2842610
## 970 1.3112225 2.6080541 1.4780532 1.8970683
## 971 0.3352981 0.7393513 0.4212767 0.6440492
## 972 0.1918581 0.3558049 0.2180213 0.1810720
## 973 0.6384296 1.3724233 0.6803522 0.6397688
## 974 1.3963724 2.5826059 1.1360771 1.9753047
## 975 1.0669564 2.5026696 1.0301152 1.1699013
## 976 1.1151084 1.7214035 1.2829008 1.8503003
## 977 0.3938340 0.7776327 0.3664632 0.3850910
## 978 0.6513355 1.4414607 0.8310974 1.2789241
## 979 0.4521065 1.0159718 0.3971504 0.6331110
## 980 0.4905416 1.0157228 0.5300665 0.4492714
## 981 0.6946290 1.2832570 0.6266537 0.5395657
## 982 1.5054391 3.1450373 1.1530744 1.2029916
## 983 0.4401047 0.8335646 0.4796253 0.5905821
## 984 0.3003470 0.4746940 0.3170447 0.3686164
## 985 1.7111694 2.8219054 2.0317382 3.3980836
## 986 1.0524659 2.1174992 1.0569779 1.2604433
## 987 2.1341109 4.8549184 2.0450703 2.2708402
## 988 0.4176621 0.9543342 0.5127675 0.6844378
## 989 2.3751047 4.7579256 1.9334818 1.9324450
## 990 0.9331670 1.9394523 0.9109838 1.0873220
## 991 0.6462386 1.4623248 0.5657779 0.8724986
## 992 0.6521340 1.2354069 0.7230086 1.0175683
## 993 0.7594492 1.1424808 0.9068972 1.3660399
## 994 1.4180220 2.3299556 1.7993201 2.5452878
## 995 0.3052074 0.6231843 0.3238777 0.4177967
## 996 1.3108126 2.4067989 1.0913945 1.8428787
## 997 1.1924435 2.6419888 1.2804028 1.4936073
## 998 0.6517871 1.2499555 0.5838490 0.7219293
## 999 1.3347185 2.9615204 1.5602537 2.4131620
## 1000 0.5503225 1.2376433 0.5433895 0.5892333boxplot(results, las=1, main="Comparación estimadores con n=1000", col = c("green","yellow","purple","blue"), names = c("Estimador1","Estimador2","Estimador3","Estimador4"))
abline(h=1, col="red") 
apply (results,2,mean)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.9992842 2.0012681 0.9954412 1.2887732apply(results,2,var)## Estimador1 Estimador2 Estimador3 Estimador4
## 0.2832402 1.2208268 0.2573689 0.5159153Los resutados indican para n=1000 el Estimador1 se puede clasificar como Insesgado, mientras que el Estimador3 como el más eficiente. Por lo que se puede concluir que el Estimador1 y el Estimador3 son los estimadores más consistente puesto que a medida que aumenta el valor de la muestra, estos se acercan al parametro definido que en este caso es 1.
Para concluir este punto, cabe aclarar que al ser aleatorios los valores, para cada simulación habrá una variación de los resultados, sin embargo, se presentaron los resultados con una de las muestras generadas.