Estimadores
WladimirAvila
2023-09-06
knitr::opts_chunk$set(echo = TRUE)
if (!require("rmarkdown")) install.packages("rmarkdown")## Loading required package: rmarkdown#install.packages("dplyr") # Install dplyr package
#library("dplyr") Ejercicio de Estimadores
En este ejericio con una distribucion exponencial para un parametro θ, se van a generar los valores de θ1,θ2,θ3,θ4, una vez esto se evaluaran las propiedades de insesgadez, eficiencia y consistencia
lo anterior se realizara con 20, 50, 100, 1000 muestras
Funciones para determinar los valores de θ
teta1 <- function(X1,X2,X3,X4){
return((X1+X2)/6+(X3+X4)/3)
}
teta2 <- function(X1,X2,X3,X4){
return((X1+(2*(X2))+(3*(X3))+(4*(X4)))/5)
}
teta3 <- function(X1,X2,X3,X4){
return((X1+X2+X3+X4)/4)
}
teta4 <- function(x){
result <- (min(x)+max(x))/2
return(result)
}
unbiasedFunction <- function (m){
return(mean(m-1))
}Desarrollo del ejercicio
Defino los DF finales que van a contener la informacion con los de todas las muestras n
columns= c("n","t1","t2","t3","t4")
unbiasedDf= data.frame(matrix(nrow = 0, ncol = length(columns)))
colnames(unbiasedDf) = columns
eficienceDf= data.frame(matrix(nrow = 0, ncol = length(columns)))
colnames(eficienceDf) = columns
set.seed(4545)
columns= c("n","t1","t2","t3","t4")
numberSamples <- list(20, 50, 100, 1000)
#numberSamples <- list(20)
data= matrix(data = rexp(1000*4,rate = 1), nrow = 1000, byrow = TRUE)
for (n in numberSamples) {
dfTeta= data.frame(matrix(nrow = 0, ncol = length(columns)))
colnames(dfTeta) = columns
myRange <- 1:n
for (i in myRange) {
x1 = (data[i,1])
x2 = (data[i,2])
x3 = (data[i,3])
x4 = (data[i,4])
valTeta1 <- teta1(x1,x2,x3,x4)
valTeta2 <- teta2(x1,x2,x3,x4)
valTeta3 <- teta3(x1,x2,x3,x4)
valTeta4 <- teta4(c(x1,x2,x3,x4))
row = list(n = n, t1=valTeta1, t2=valTeta2, t3=valTeta3, t4=valTeta4)
dfTeta = rbind(dfTeta, row)
}
# tst= paged_table(dfTeta, options = NULL)
print(dfTeta)
boxplot(dfTeta[1:n,2:5], col = c("red", "green", "blue", "purple"), main = paste("Comportamiento de los estimadores para n ", n ))
legend("topleft", legend = c("e1", "e2", "e3", "e4"), col = c("red", "green", "blue", "purple"), lty = 1, cex = 0.8)
abline(h=1, col="red")
#insesgadez
unbiased =apply(X = dfTeta[1:n,2:5], MARGIN=2, FUN = unbiasedFunction)
row = list(n = n, t1=unbiased['t1'], t2=unbiased['t2'], t3=unbiased['t3'], t4=unbiased['t4'])
unbiasedDf <- rbind(unbiasedDf, row)
#eficiencia
eficience= apply(X = dfTeta[1:n,2:5], MARGIN=2, FUN = var)
row = list(n = n, t1=eficience['t1'], t2=eficience['t2'], t3=eficience['t3'], t4=eficience['t4'])
eficienceDf <- rbind(eficienceDf, row)
}## n t1 t2 t3 t4
## 1 20 1.5271095 3.080612 1.5737529 1.4611260
## 2 20 1.0289978 1.954063 0.9533463 1.1803008
## 3 20 0.8415452 1.765738 0.8703700 0.9568446
## 4 20 1.4024634 2.537636 1.2784217 1.6505466
## 5 20 1.0405874 2.130273 1.1543805 1.3909195
## 6 20 0.4927914 1.091658 0.5900513 0.8491121
## 7 20 1.4754537 2.570642 1.6091538 1.2614284
## 8 20 1.9567828 4.478114 2.0100933 2.1700246
## 9 20 1.4048366 2.777874 1.1995470 1.4843347
## 10 20 1.4933970 3.293505 1.5850554 1.8600307
## 11 20 1.5996666 3.068829 1.5692218 1.4778873
## 12 20 2.0490675 4.448241 2.0209884 2.1052259
## 13 20 0.9782413 1.828527 0.8138934 1.0122544
## 14 20 1.4354769 3.060518 1.1273551 1.2931445
## 15 20 0.6391117 1.443461 0.8362078 1.2043859
## 16 20 1.0411834 2.113220 0.9540646 0.9440780
## 17 20 0.8000421 1.418509 0.7536116 0.8929030
## 18 20 0.8970349 1.461786 1.0647600 1.2837420
## 19 20 0.8813811 1.728010 0.9050066 0.8417508
## 20 20 0.9438491 2.035279 1.3371756 2.0994544
## n t1 t2 t3 t4
## 1 50 1.5271095 3.0806125 1.5737529 1.4611260
## 2 50 1.0289978 1.9540629 0.9533463 1.1803008
## 3 50 0.8415452 1.7657384 0.8703700 0.9568446
## 4 50 1.4024634 2.5376365 1.2784217 1.6505466
## 5 50 1.0405874 2.1302730 1.1543805 1.3909195
## 6 50 0.4927914 1.0916584 0.5900513 0.8491121
## 7 50 1.4754537 2.5706419 1.6091538 1.2614284
## 8 50 1.9567828 4.4781142 2.0100933 2.1700246
## 9 50 1.4048366 2.7778739 1.1995470 1.4843347
## 10 50 1.4933970 3.2935053 1.5850554 1.8600307
## 11 50 1.5996666 3.0688289 1.5692218 1.4778873
## 12 50 2.0490675 4.4482415 2.0209884 2.1052259
## 13 50 0.9782413 1.8285267 0.8138934 1.0122544
## 14 50 1.4354769 3.0605183 1.1273551 1.2931445
## 15 50 0.6391117 1.4434610 0.8362078 1.2043859
## 16 50 1.0411834 2.1132196 0.9540646 0.9440780
## 17 50 0.8000421 1.4185090 0.7536116 0.8929030
## 18 50 0.8970349 1.4617855 1.0647600 1.2837420
## 19 50 0.8813811 1.7280096 0.9050066 0.8417508
## 20 50 0.9438491 2.0352790 1.3371756 2.0994544
## 21 50 0.5063491 1.0183341 0.4502215 0.4922590
## 22 50 0.8858256 2.1004611 0.8248350 1.0078067
## 23 50 1.7466409 3.4620358 1.7116007 1.6064801
## 24 50 0.3381500 0.7026088 0.3433136 0.3588043
## 25 50 0.7993277 1.6057716 0.7063264 0.7815372
## 26 50 0.7875795 1.6049505 0.6412024 0.7131008
## 27 50 1.5175045 3.0750203 1.4304520 1.4434278
## 28 50 0.6637766 1.1672014 0.7225914 0.8990356
## 29 50 0.4597214 0.9747302 0.4420863 0.4949915
## 30 50 0.9650304 1.7389224 0.8329468 1.1738140
## 31 50 0.2099749 0.4001905 0.2231833 0.2593731
## 32 50 0.7667789 1.4906381 0.6310522 0.7673514
## 33 50 0.4423262 0.8891958 0.6064844 0.7820014
## 34 50 1.4569881 3.1404374 1.6009302 1.2265883
## 35 50 0.9898457 2.2852121 0.9000657 1.1694056
## 36 50 2.5836555 5.1328176 2.8249035 2.7722854
## 37 50 0.6072229 1.0982119 0.6243988 0.5728711
## 38 50 1.2592349 2.9416388 1.2187586 1.3367956
## 39 50 1.0581762 1.9689015 1.0938229 1.1171781
## 40 50 0.5704300 1.3225377 0.4991118 0.7130665
## 41 50 0.4812094 0.7466750 0.6743254 1.0205689
## 42 50 0.8185633 1.4753132 0.7455499 0.9422529
## 43 50 0.6304708 1.1533807 0.8499677 0.8993731
## 44 50 1.3827647 3.1320319 1.1099302 1.7533522
## 45 50 1.3421711 2.5330555 1.2579268 1.5106596
## 46 50 2.1909706 3.9041686 2.2840077 2.0048964
## 47 50 1.3733461 2.3559108 1.5153803 1.6804503
## 48 50 0.8672566 1.6727921 0.7666680 1.0215596
## 49 50 2.0132920 4.1656342 1.6265931 1.6481132
## 50 50 0.7545333 1.4332232 0.6924038 0.8787922
## n t1 t2 t3 t4
## 1 100 1.5271095 3.0806125 1.5737529 1.4611260
## 2 100 1.0289978 1.9540629 0.9533463 1.1803008
## 3 100 0.8415452 1.7657384 0.8703700 0.9568446
## 4 100 1.4024634 2.5376365 1.2784217 1.6505466
## 5 100 1.0405874 2.1302730 1.1543805 1.3909195
## 6 100 0.4927914 1.0916584 0.5900513 0.8491121
## 7 100 1.4754537 2.5706419 1.6091538 1.2614284
## 8 100 1.9567828 4.4781142 2.0100933 2.1700246
## 9 100 1.4048366 2.7778739 1.1995470 1.4843347
## 10 100 1.4933970 3.2935053 1.5850554 1.8600307
## 11 100 1.5996666 3.0688289 1.5692218 1.4778873
## 12 100 2.0490675 4.4482415 2.0209884 2.1052259
## 13 100 0.9782413 1.8285267 0.8138934 1.0122544
## 14 100 1.4354769 3.0605183 1.1273551 1.2931445
## 15 100 0.6391117 1.4434610 0.8362078 1.2043859
## 16 100 1.0411834 2.1132196 0.9540646 0.9440780
## 17 100 0.8000421 1.4185090 0.7536116 0.8929030
## 18 100 0.8970349 1.4617855 1.0647600 1.2837420
## 19 100 0.8813811 1.7280096 0.9050066 0.8417508
## 20 100 0.9438491 2.0352790 1.3371756 2.0994544
## 21 100 0.5063491 1.0183341 0.4502215 0.4922590
## 22 100 0.8858256 2.1004611 0.8248350 1.0078067
## 23 100 1.7466409 3.4620358 1.7116007 1.6064801
## 24 100 0.3381500 0.7026088 0.3433136 0.3588043
## 25 100 0.7993277 1.6057716 0.7063264 0.7815372
## 26 100 0.7875795 1.6049505 0.6412024 0.7131008
## 27 100 1.5175045 3.0750203 1.4304520 1.4434278
## 28 100 0.6637766 1.1672014 0.7225914 0.8990356
## 29 100 0.4597214 0.9747302 0.4420863 0.4949915
## 30 100 0.9650304 1.7389224 0.8329468 1.1738140
## 31 100 0.2099749 0.4001905 0.2231833 0.2593731
## 32 100 0.7667789 1.4906381 0.6310522 0.7673514
## 33 100 0.4423262 0.8891958 0.6064844 0.7820014
## 34 100 1.4569881 3.1404374 1.6009302 1.2265883
## 35 100 0.9898457 2.2852121 0.9000657 1.1694056
## 36 100 2.5836555 5.1328176 2.8249035 2.7722854
## 37 100 0.6072229 1.0982119 0.6243988 0.5728711
## 38 100 1.2592349 2.9416388 1.2187586 1.3367956
## 39 100 1.0581762 1.9689015 1.0938229 1.1171781
## 40 100 0.5704300 1.3225377 0.4991118 0.7130665
## 41 100 0.4812094 0.7466750 0.6743254 1.0205689
## 42 100 0.8185633 1.4753132 0.7455499 0.9422529
## 43 100 0.6304708 1.1533807 0.8499677 0.8993731
## 44 100 1.3827647 3.1320319 1.1099302 1.7533522
## 45 100 1.3421711 2.5330555 1.2579268 1.5106596
## 46 100 2.1909706 3.9041686 2.2840077 2.0048964
## 47 100 1.3733461 2.3559108 1.5153803 1.6804503
## 48 100 0.8672566 1.6727921 0.7666680 1.0215596
## 49 100 2.0132920 4.1656342 1.6265931 1.6481132
## 50 100 0.7545333 1.4332232 0.6924038 0.8787922
## 51 100 0.7687249 1.6564100 0.6669871 0.8626500
## 52 100 1.8113131 3.8988471 2.0986995 2.4891886
## 53 100 0.4733722 0.8579333 0.5424712 0.4860371
## 54 100 1.1884885 2.6457936 0.9224005 1.3169242
## 55 100 0.4480066 0.7728891 0.5414230 0.5032303
## 56 100 1.3072776 2.8838603 1.3231682 1.2754964
## 57 100 1.0377644 2.3173809 0.9286682 1.2559570
## 58 100 0.3926378 0.6296770 0.4945389 0.7816340
## 59 100 0.7291793 1.5662319 0.5790696 0.6175323
## 60 100 0.6509909 1.0894769 0.7146671 0.8120277
## 61 100 1.2119382 2.4798427 1.2698591 1.0960963
## 62 100 1.2262214 2.8045621 1.0141961 1.5397363
## 63 100 1.8343892 3.7534493 1.5350682 1.4474242
## 64 100 0.6641206 1.3117709 0.9199287 1.1315988
## 65 100 1.1792418 2.4858256 1.1231413 0.9548398
## 66 100 0.7785250 1.7556724 0.6104271 0.9388849
## 67 100 1.0837290 2.5268076 0.8499717 1.3999028
## 68 100 0.4277673 0.7330747 0.4213395 0.4406231
## 69 100 0.9367814 2.0460065 0.8198575 0.8935333
## 70 100 0.2518766 0.5188633 0.2810043 0.3479070
## 71 100 0.7979439 1.8498389 0.7027380 0.9883555
## 72 100 0.6779036 1.3212709 0.8046738 0.7642446
## 73 100 0.7497940 1.3946730 0.8396479 1.0120815
## 74 100 2.0811097 4.1432740 2.2261190 2.2191543
## 75 100 1.2059976 2.5705199 1.0292433 1.2488010
## 76 100 1.2231724 2.4899416 1.3102546 1.1910898
## 77 100 1.3576328 2.6269012 1.3785744 1.3772966
## 78 100 0.6926200 1.2443623 0.7356273 0.6655707
## 79 100 0.7312278 1.5519694 0.7661688 0.8709919
## 80 100 0.5777780 1.1293072 0.6106054 0.5947730
## 81 100 0.3522892 0.7064249 0.2853566 0.3476730
## 82 100 0.9352640 1.9871864 1.1117558 1.5798935
## 83 100 0.9567705 2.1926565 0.8188322 1.0023488
## 84 100 0.5405505 1.2052973 0.4541959 0.6783322
## 85 100 1.2266220 2.6379570 1.2410118 1.2841812
## 86 100 0.5934084 1.2134784 0.5005221 0.5267546
## 87 100 0.7280970 1.3725371 0.6896004 0.8050901
## 88 100 0.4244477 0.9995042 0.3543604 0.5646225
## 89 100 0.3879464 0.7627466 0.3111203 0.4208121
## 90 100 0.7325797 1.3197503 0.7858669 0.6971409
## 91 100 0.6667992 1.2473845 0.6276404 0.7451168
## 92 100 1.1655069 2.4627373 1.1889364 1.1186479
## 93 100 1.3331725 2.8842934 1.2755095 1.3919452
## 94 100 1.1547023 2.0385871 1.0881462 1.2878145
## 95 100 0.2205417 0.3738233 0.2244279 0.2359874
## 96 100 0.6681805 1.3159028 0.7291664 0.7390072
## 97 100 1.6942995 3.7214582 1.3899327 1.9177138
## 98 100 2.4698747 5.0159486 2.0917097 2.2390624
## 99 100 1.1557893 2.5238741 1.0539377 1.2372002
## 100 100 0.4391477 0.8487255 0.3912401 0.4488410
## n t1 t2 t3 t4
## 1 1000 1.52710953 3.0806125 1.5737529 1.4611260
## 2 1000 1.02899781 1.9540629 0.9533463 1.1803008
## 3 1000 0.84154517 1.7657384 0.8703700 0.9568446
## 4 1000 1.40246336 2.5376365 1.2784217 1.6505466
## 5 1000 1.04058736 2.1302730 1.1543805 1.3909195
## 6 1000 0.49279139 1.0916584 0.5900513 0.8491121
## 7 1000 1.47545370 2.5706419 1.6091538 1.2614284
## 8 1000 1.95678284 4.4781142 2.0100933 2.1700246
## 9 1000 1.40483658 2.7778739 1.1995470 1.4843347
## 10 1000 1.49339698 3.2935053 1.5850554 1.8600307
## 11 1000 1.59966665 3.0688289 1.5692218 1.4778873
## 12 1000 2.04906755 4.4482415 2.0209884 2.1052259
## 13 1000 0.97824131 1.8285267 0.8138934 1.0122544
## 14 1000 1.43547694 3.0605183 1.1273551 1.2931445
## 15 1000 0.63911172 1.4434610 0.8362078 1.2043859
## 16 1000 1.04118335 2.1132196 0.9540646 0.9440780
## 17 1000 0.80004210 1.4185090 0.7536116 0.8929030
## 18 1000 0.89703490 1.4617855 1.0647600 1.2837420
## 19 1000 0.88138110 1.7280096 0.9050066 0.8417508
## 20 1000 0.94384906 2.0352790 1.3371756 2.0994544
## 21 1000 0.50634905 1.0183341 0.4502215 0.4922590
## 22 1000 0.88582556 2.1004611 0.8248350 1.0078067
## 23 1000 1.74664093 3.4620358 1.7116007 1.6064801
## 24 1000 0.33814997 0.7026088 0.3433136 0.3588043
## 25 1000 0.79932770 1.6057716 0.7063264 0.7815372
## 26 1000 0.78757952 1.6049505 0.6412024 0.7131008
## 27 1000 1.51750448 3.0750203 1.4304520 1.4434278
## 28 1000 0.66377664 1.1672014 0.7225914 0.8990356
## 29 1000 0.45972136 0.9747302 0.4420863 0.4949915
## 30 1000 0.96503036 1.7389224 0.8329468 1.1738140
## 31 1000 0.20997490 0.4001905 0.2231833 0.2593731
## 32 1000 0.76677889 1.4906381 0.6310522 0.7673514
## 33 1000 0.44232617 0.8891958 0.6064844 0.7820014
## 34 1000 1.45698814 3.1404374 1.6009302 1.2265883
## 35 1000 0.98984566 2.2852121 0.9000657 1.1694056
## 36 1000 2.58365548 5.1328176 2.8249035 2.7722854
## 37 1000 0.60722293 1.0982119 0.6243988 0.5728711
## 38 1000 1.25923487 2.9416388 1.2187586 1.3367956
## 39 1000 1.05817617 1.9689015 1.0938229 1.1171781
## 40 1000 0.57043001 1.3225377 0.4991118 0.7130665
## 41 1000 0.48120939 0.7466750 0.6743254 1.0205689
## 42 1000 0.81856334 1.4753132 0.7455499 0.9422529
## 43 1000 0.63047081 1.1533807 0.8499677 0.8993731
## 44 1000 1.38276465 3.1320319 1.1099302 1.7533522
## 45 1000 1.34217106 2.5330555 1.2579268 1.5106596
## 46 1000 2.19097058 3.9041686 2.2840077 2.0048964
## 47 1000 1.37334614 2.3559108 1.5153803 1.6804503
## 48 1000 0.86725664 1.6727921 0.7666680 1.0215596
## 49 1000 2.01329200 4.1656342 1.6265931 1.6481132
## 50 1000 0.75453326 1.4332232 0.6924038 0.8787922
## 51 1000 0.76872485 1.6564100 0.6669871 0.8626500
## 52 1000 1.81131306 3.8988471 2.0986995 2.4891886
## 53 1000 0.47337225 0.8579333 0.5424712 0.4860371
## 54 1000 1.18848854 2.6457936 0.9224005 1.3169242
## 55 1000 0.44800658 0.7728891 0.5414230 0.5032303
## 56 1000 1.30727762 2.8838603 1.3231682 1.2754964
## 57 1000 1.03776445 2.3173809 0.9286682 1.2559570
## 58 1000 0.39263776 0.6296770 0.4945389 0.7816340
## 59 1000 0.72917927 1.5662319 0.5790696 0.6175323
## 60 1000 0.65099093 1.0894769 0.7146671 0.8120277
## 61 1000 1.21193816 2.4798427 1.2698591 1.0960963
## 62 1000 1.22622135 2.8045621 1.0141961 1.5397363
## 63 1000 1.83438925 3.7534493 1.5350682 1.4474242
## 64 1000 0.66412059 1.3117709 0.9199287 1.1315988
## 65 1000 1.17924184 2.4858256 1.1231413 0.9548398
## 66 1000 0.77852503 1.7556724 0.6104271 0.9388849
## 67 1000 1.08372896 2.5268076 0.8499717 1.3999028
## 68 1000 0.42776735 0.7330747 0.4213395 0.4406231
## 69 1000 0.93678144 2.0460065 0.8198575 0.8935333
## 70 1000 0.25187663 0.5188633 0.2810043 0.3479070
## 71 1000 0.79794386 1.8498389 0.7027380 0.9883555
## 72 1000 0.67790364 1.3212709 0.8046738 0.7642446
## 73 1000 0.74979399 1.3946730 0.8396479 1.0120815
## 74 1000 2.08110968 4.1432740 2.2261190 2.2191543
## 75 1000 1.20599755 2.5705199 1.0292433 1.2488010
## 76 1000 1.22317237 2.4899416 1.3102546 1.1910898
## 77 1000 1.35763281 2.6269012 1.3785744 1.3772966
## 78 1000 0.69261998 1.2443623 0.7356273 0.6655707
## 79 1000 0.73122775 1.5519694 0.7661688 0.8709919
## 80 1000 0.57777802 1.1293072 0.6106054 0.5947730
## 81 1000 0.35228921 0.7064249 0.2853566 0.3476730
## 82 1000 0.93526402 1.9871864 1.1117558 1.5798935
## 83 1000 0.95677054 2.1926565 0.8188322 1.0023488
## 84 1000 0.54055049 1.2052973 0.4541959 0.6783322
## 85 1000 1.22662197 2.6379570 1.2410118 1.2841812
## 86 1000 0.59340843 1.2134784 0.5005221 0.5267546
## 87 1000 0.72809698 1.3725371 0.6896004 0.8050901
## 88 1000 0.42444774 0.9995042 0.3543604 0.5646225
## 89 1000 0.38794643 0.7627466 0.3111203 0.4208121
## 90 1000 0.73257974 1.3197503 0.7858669 0.6971409
## 91 1000 0.66679922 1.2473845 0.6276404 0.7451168
## 92 1000 1.16550693 2.4627373 1.1889364 1.1186479
## 93 1000 1.33317254 2.8842934 1.2755095 1.3919452
## 94 1000 1.15470228 2.0385871 1.0881462 1.2878145
## 95 1000 0.22054167 0.3738233 0.2244279 0.2359874
## 96 1000 0.66818045 1.3159028 0.7291664 0.7390072
## 97 1000 1.69429954 3.7214582 1.3899327 1.9177138
## 98 1000 2.46987469 5.0159486 2.0917097 2.2390624
## 99 1000 1.15578932 2.5238741 1.0539377 1.2372002
## 100 1000 0.43914774 0.8487255 0.3912401 0.4488410
## 101 1000 1.42774678 2.8005390 1.3715574 1.5401254
## 102 1000 1.59348969 3.2223472 1.6724771 1.8116867
## 103 1000 1.61024854 3.6538140 1.4107207 1.9704551
## 104 1000 1.33789714 2.7188489 1.3900516 1.2335883
## 105 1000 1.14619219 2.0917255 1.1534079 1.1317607
## 106 1000 0.67640590 1.1039197 0.9167744 1.2986362
## 107 1000 1.33163178 2.4806081 1.3041488 1.2217000
## 108 1000 1.68195633 3.1378661 1.4211694 1.7643871
## 109 1000 1.93666286 3.4669893 2.1642348 1.6780904
## 110 1000 1.00707493 1.8600034 1.3585133 1.3245854
## 111 1000 0.86529189 1.7324939 0.7674459 0.6743754
## 112 1000 0.81685897 1.5245499 0.9813624 1.0897791
## 113 1000 1.17992490 2.2067344 1.2296959 1.3227108
## 114 1000 0.56417791 0.9811539 0.5666023 0.5738753
## 115 1000 0.51057615 1.0944384 0.3863069 0.4452529
## 116 1000 2.65153261 5.1295376 2.4895736 2.9754507
## 117 1000 0.53080142 1.2388222 0.4873500 0.5485829
## 118 1000 1.83692849 3.8499385 1.5182866 1.4049879
## 119 1000 1.05866477 1.8366972 1.1925226 1.4233210
## 120 1000 0.86166753 1.5651759 0.9570221 0.6709584
## 121 1000 1.46520682 2.5727460 1.7135695 2.3593759
## 122 1000 2.19339969 5.1502933 1.7005090 2.9981176
## 123 1000 1.38766367 3.0623146 1.1525654 1.2634697
## 124 1000 1.78998492 3.3892951 1.6650192 1.4079318
## 125 1000 1.23081108 2.5245605 1.0452423 1.0734651
## 126 1000 1.16844201 2.3838922 1.0859420 1.0509216
## 127 1000 2.02683070 3.9279262 1.8135470 2.3411687
## 128 1000 1.63713476 3.0032634 1.2960545 2.2728961
## 129 1000 0.80871456 1.7191341 0.7281555 0.8223514
## 130 1000 0.90276274 2.0415257 1.0370437 1.1466658
## 131 1000 1.06512075 2.4006482 1.0326941 1.1299740
## 132 1000 0.71071829 1.4303928 0.6957875 0.7032472
## 133 1000 0.42920082 0.9051916 0.5028492 0.5933930
## 134 1000 1.09633809 2.5243862 0.9408975 1.2126798
## 135 1000 2.80010527 6.2550560 2.9128711 3.2511684
## 136 1000 1.43677923 3.1970402 1.8334559 2.4885305
## 137 1000 2.05023404 3.8412475 2.2347136 2.6982855
## 138 1000 0.74158736 1.6846346 1.0173329 1.7620423
## 139 1000 0.54370471 1.0885562 0.6529109 0.5408376
## 140 1000 1.89348683 3.4419235 1.5461531 2.4802674
## 141 1000 0.87086082 1.4545568 1.1570770 1.5887729
## 142 1000 2.29374036 5.3878593 1.8137127 3.2387945
## 143 1000 1.32421057 2.6387773 1.4796943 1.3483201
## 144 1000 1.33749336 2.4513384 1.1479842 1.5547300
## 145 1000 1.38253069 3.2549850 1.0685936 1.9491463
## 146 1000 1.39183867 2.5144181 1.1245536 1.9264088
## 147 1000 1.28000848 2.4557162 1.4070605 1.2733605
## 148 1000 0.33138653 0.7200678 0.2752119 0.3622741
## 149 1000 0.71521484 1.3709010 0.5979763 0.6743567
## 150 1000 0.91481578 1.8318047 1.0286867 1.1479904
## 151 1000 1.19721408 2.6962598 0.9346609 1.4266869
## 152 1000 0.80809513 1.7956223 0.6396512 0.8110855
## 153 1000 1.63230316 3.1858727 1.7179502 1.6067631
## 154 1000 0.36130417 0.6797770 0.3257899 0.3075592
## 155 1000 1.40358835 3.0640819 1.4118855 1.4256238
## 156 1000 0.97915921 2.2221970 1.1058681 1.2246299
## 157 1000 0.74969795 1.5991612 0.8424577 1.1207370
## 158 1000 0.71916888 1.5337345 0.6411226 0.6365009
## 159 1000 1.92928151 3.9665326 1.8063493 1.9533410
## 160 1000 1.13636269 2.4405673 1.4262554 2.1357530
## 161 1000 1.01048539 2.1992529 0.8214495 1.0781189
## 162 1000 0.91940862 2.0465507 0.9704174 1.1234438
## 163 1000 1.81885971 4.2372870 1.4507761 2.3696361
## 164 1000 0.99184915 2.0905974 0.9487175 1.0781124
## 165 1000 1.63304452 3.2104963 1.4838006 1.7720263
## 166 1000 0.84102789 1.6283680 0.8132192 0.7297931
## 167 1000 0.88108761 1.9136850 0.8700701 0.9031227
## 168 1000 1.27198397 2.8925110 1.1975096 1.3640528
## 169 1000 0.35541716 0.7420645 0.4174460 0.4255937
## 170 1000 0.52571832 0.9034968 0.5929573 0.7946741
## 171 1000 2.07252429 4.3315415 1.9397578 1.6062920
## 172 1000 0.73997412 1.5927645 0.6172250 0.6994167
## 173 1000 1.45017320 2.7983391 1.2935184 1.6259286
## 174 1000 0.87048910 1.8762419 0.6931251 0.8539203
## 175 1000 1.43387866 2.7311449 1.1225476 1.6888767
## 176 1000 0.43506297 0.8570169 0.3926030 0.4678356
## 177 1000 0.74892974 1.6385697 0.6490759 0.6298119
## 178 1000 0.50087809 0.9649419 0.4284327 0.5929138
## 179 1000 0.67049089 1.0835643 0.6854407 0.7133899
## 180 1000 1.00723646 2.0717548 0.9178572 0.9716828
## 181 1000 1.56277536 3.1952671 1.3872772 1.3884843
## 182 1000 0.94686437 2.0974935 0.8033155 1.1691787
## 183 1000 0.40889360 0.7053991 0.4098731 0.4128118
## 184 1000 1.16849742 2.5647448 1.1396166 1.0529740
## 185 1000 0.72229563 1.6003978 0.8320751 1.1614135
## 186 1000 0.60480212 1.0991050 0.8401434 0.8810503
## 187 1000 0.59543392 1.2008215 0.6299395 0.5705498
## 188 1000 1.08316484 1.8639370 0.9701268 1.3092410
## 189 1000 0.98544488 1.9573796 1.0273848 1.0355493
## 190 1000 1.18325864 2.4633324 1.3255962 1.7099714
## 191 1000 0.93451691 1.8934019 0.7832960 0.8735966
## 192 1000 0.49333839 0.8511033 0.5635225 0.5133241
## 193 1000 1.57221398 3.6067713 1.4407192 1.8032673
## 194 1000 1.10654201 2.3953534 0.9088688 1.1668691
## 195 1000 0.70030428 1.5591068 0.5813004 0.6680707
## 196 1000 0.96670513 1.9364968 1.0299952 0.9589887
## 197 1000 0.65301388 1.3189133 0.7979900 0.9751800
## 198 1000 0.74011234 1.3700742 0.7266366 0.7670639
## 199 1000 1.28988108 2.7013522 1.2522827 1.1394875
## 200 1000 0.78748231 1.4040930 0.7054577 0.8091761
## 201 1000 1.19949494 2.1971596 1.2675721 1.2369399
## 202 1000 0.72695297 1.0996426 0.9197854 1.4982828
## 203 1000 1.36398016 2.9036134 1.3010083 1.1611389
## 204 1000 0.44417064 0.8272905 0.4806700 0.5901681
## 205 1000 0.56904109 1.0012454 0.4699621 0.7489900
## 206 1000 0.53350704 0.9571683 0.5716513 0.6860841
## 207 1000 1.42283974 2.3856106 1.4470707 1.3743778
## 208 1000 1.51089143 2.8591662 1.3512791 1.7888987
## 209 1000 1.22244990 2.5073931 1.0295677 0.9929187
## 210 1000 0.47572671 1.0513699 0.6202794 0.9269640
## 211 1000 0.53924408 1.2023326 0.5174536 0.5565012
## 212 1000 0.65871630 1.4597926 0.6668651 0.6424187
## 213 1000 0.28159992 0.5651633 0.3088484 0.3410057
## 214 1000 1.01287234 1.4892482 1.3038304 2.1767045
## 215 1000 1.76604487 3.0727223 1.6604823 1.7232488
## 216 1000 0.51296345 0.9832865 0.5697579 0.5199513
## 217 1000 1.57962589 3.4759059 1.3500248 1.9120589
## 218 1000 0.80052804 1.6016890 0.7428220 0.7989458
## 219 1000 0.42553633 0.9349146 0.5658582 0.8229877
## 220 1000 2.10939479 3.9027713 1.8339164 2.6398302
## 221 1000 1.30348225 2.7734983 1.4435068 1.4718275
## 222 1000 0.50698504 0.8777524 0.5287229 0.5939363
## 223 1000 0.90197521 1.7226878 0.8147195 1.0764866
## 224 1000 0.24563128 0.4945148 0.2255380 0.2375007
## 225 1000 0.91015808 2.0743215 0.7256695 1.0947628
## 226 1000 1.24916828 2.1061660 1.1984149 1.3506751
## 227 1000 0.97031318 2.1670024 0.9391891 1.0325612
## 228 1000 1.01650179 1.8208054 0.9475531 1.0023995
## 229 1000 0.82268708 1.4196158 0.8962789 1.0731164
## 230 1000 0.50789525 1.0563142 0.6871197 0.9676534
## 231 1000 1.05355577 2.1007630 1.1982421 1.0694271
## 232 1000 0.82530841 1.8160161 0.8056737 0.8645779
## 233 1000 1.06474074 2.0872622 1.0027876 0.8352862
## 234 1000 0.52517159 1.0216066 0.4111038 0.5970129
## 235 1000 1.62458295 3.2254902 1.9640031 2.0785289
## 236 1000 0.76736332 1.4111370 1.0621120 1.0478866
## 237 1000 1.12086422 1.9626073 1.3709462 1.6970118
## 238 1000 1.47598638 3.0346219 1.5312182 1.6969137
## 239 1000 0.58437284 1.1866823 0.5217023 0.5395312
## 240 1000 1.06386405 2.2588987 0.9761279 0.7359376
## 241 1000 1.13684483 2.2573304 1.4352836 1.6928243
## 242 1000 1.45551018 3.0203701 1.2785985 1.3750612
## 243 1000 1.30642258 2.2773037 1.6299843 2.1452762
## 244 1000 0.66987250 1.4474026 0.8043441 0.9901106
## 245 1000 0.86778052 1.8636387 0.9526405 1.2072205
## 246 1000 1.51602574 3.0545649 1.2074457 1.4597421
## 247 1000 0.53214101 0.9403017 0.7321226 0.8420917
## 248 1000 0.51035758 0.9249256 0.6325483 0.5174675
## 249 1000 0.64194360 1.4183929 0.5892813 0.5940942
## 250 1000 0.47001988 0.9633164 0.4154586 0.4118283
## 251 1000 0.42119607 0.8422816 0.3828218 0.4214723
## 252 1000 0.99242964 1.7399739 1.0282487 1.1038890
## 253 1000 0.86478902 2.0550107 0.6981323 1.1914964
## 254 1000 1.25037990 2.5945179 1.1909774 1.3659700
## 255 1000 0.33277184 0.6778052 0.3888616 0.4021412
## 256 1000 1.68593671 3.5524801 1.5806211 1.5337367
## 257 1000 2.01825492 3.7372417 2.1324063 2.3094206
## 258 1000 2.11892704 4.8329658 1.9318735 2.4930340
## 259 1000 0.79816719 1.7742400 0.6532351 0.9530672
## 260 1000 0.91954501 1.7943715 1.2304291 1.3428213
## 261 1000 1.11022069 2.4178669 1.5470867 2.4775165
## 262 1000 0.58033462 1.1111533 0.6678351 0.7041245
## 263 1000 0.72089362 1.4104326 0.7881112 0.7992802
## 264 1000 0.50014647 0.7892488 0.6759317 0.9810995
## 265 1000 0.58905899 0.9360193 0.7521644 1.1943056
## 266 1000 1.44759902 2.4592455 1.6312444 1.4618722
## 267 1000 2.10734999 4.1511581 1.8132416 1.8936404
## 268 1000 0.85739648 1.8076700 0.7638243 0.6252039
## 269 1000 0.63028071 1.4689689 0.5759181 0.6863084
## 270 1000 1.32661876 2.7614252 1.0926908 1.1292319
## 271 1000 0.50664848 0.8799857 0.4965017 0.5269420
## 272 1000 0.85662766 1.8212988 0.7349516 0.8833842
## 273 1000 0.59453142 1.2940437 0.6842987 0.8427741
## 274 1000 1.70242548 3.5425548 1.3855603 1.4129547
## 275 1000 1.10589106 2.1502773 1.1707146 1.1673664
## 276 1000 0.42868521 0.8636506 0.4227297 0.4324745
## 277 1000 0.49511791 1.1380840 0.6046879 0.9333980
## 278 1000 0.78275234 1.7025941 0.6455608 0.7222788
## 279 1000 1.34634067 2.4882725 1.2278935 1.2186500
## 280 1000 0.30748053 0.4995791 0.3958971 0.5959355
## 281 1000 1.87481050 4.1712262 1.7251960 1.4419602
## 282 1000 0.82919536 1.5587507 0.6835840 1.0552416
## 283 1000 0.55679924 1.1222796 0.6841908 0.7307863
## 284 1000 0.93727187 1.9083769 1.0663787 0.8526889
## 285 1000 0.19982744 0.4317518 0.2669953 0.4144054
## 286 1000 2.09766569 4.5157370 1.8860734 2.1294342
## 287 1000 0.58804732 1.1944588 0.5829703 0.5982014
## 288 1000 0.52601136 1.0447453 0.4705360 0.5442049
## 289 1000 0.59038418 1.1872551 0.7120881 0.8500089
## 290 1000 1.59049897 3.1891276 1.5431663 1.5161577
## 291 1000 1.03136456 2.1791550 0.8804345 0.7402999
## 292 1000 1.43969004 2.8849033 1.4092326 1.4258821
## 293 1000 1.38829819 2.0975860 1.6872442 2.3261570
## 294 1000 0.12640491 0.2622874 0.1177844 0.1328579
## 295 1000 0.73550873 1.2390410 0.8133763 0.8959100
## 296 1000 1.93385227 3.6146171 1.9995772 2.1967519
## 297 1000 0.40346920 0.8731430 0.4449955 0.3559866
## 298 1000 0.93558716 1.8716176 0.7855791 0.7835372
## 299 1000 0.68799450 1.4435277 0.6202453 0.5191479
## 300 1000 0.98580379 1.7101295 1.0330626 1.1748391
## 301 1000 1.90912759 2.9764716 2.1981753 2.8644217
## 302 1000 1.49756567 3.4094097 1.3951045 1.6750756
## 303 1000 0.50296486 0.9216286 0.5613383 0.7137177
## 304 1000 0.45984123 0.8066475 0.5508820 0.4930219
## 305 1000 0.54887017 1.2176878 0.6767245 0.8427860
## 306 1000 1.02207776 1.7055993 1.1338474 1.2638796
## 307 1000 0.66808292 1.2959791 0.7920882 0.7981545
## 308 1000 1.27439654 2.3422062 1.4967426 1.5984373
## 309 1000 1.29931232 2.4414921 1.1788028 1.4906042
## 310 1000 0.64312194 1.1821405 0.6579469 0.6883486
## 311 1000 0.99879535 1.8542099 1.0846792 1.0868243
## 312 1000 0.25455464 0.4801064 0.2071716 0.3270618
## 313 1000 0.55048075 1.0939116 0.4458103 0.4367569
## 314 1000 0.78472057 1.4840420 0.9807205 0.9982183
## 315 1000 1.44691936 2.4997914 1.4096116 1.4560412
## 316 1000 1.15322255 2.0573891 1.1494087 1.1379671
## 317 1000 0.92826069 1.9027330 0.9640764 0.8566293
## 318 1000 0.33117840 0.6217614 0.3325206 0.3284941
## 319 1000 0.96714565 2.0812416 1.0858063 1.4114842
## 320 1000 0.68324967 1.3793100 0.6673033 0.6512230
## 321 1000 0.50736180 1.0515134 0.5904202 0.5803910
## 322 1000 0.52114357 0.9475346 0.6001553 0.6857135
## 323 1000 0.46915334 0.7791931 0.6161736 0.7862912
## 324 1000 1.29654025 2.5029078 1.1384099 1.0737622
## 325 1000 0.12159817 0.2356290 0.1004506 0.1405165
## 326 1000 0.25851251 0.4763971 0.2099248 0.3556879
## 327 1000 1.38487054 2.7252590 1.3569661 1.2750764
## 328 1000 1.27933498 2.5480085 1.4239457 1.5419027
## 329 1000 1.31966718 2.5981903 1.1164035 1.3398406
## 330 1000 1.00898529 1.9943947 1.0596794 1.0514338
## 331 1000 0.89910155 1.9399566 1.0735463 1.5968807
## 332 1000 1.01145060 1.8738114 0.9505571 1.1332377
## 333 1000 1.19745211 2.4823624 1.0319326 1.0850584
## 334 1000 1.20963326 2.4411306 1.0569196 0.9588663
## 335 1000 0.74900893 1.5353654 0.8904165 0.8589780
## 336 1000 0.53763357 0.9050391 0.6347076 0.8869231
## 337 1000 0.54364129 1.0129794 0.7203722 0.7293993
## 338 1000 1.62115838 3.7216751 1.6318008 1.5998736
## 339 1000 1.57209360 2.7314574 1.3786325 1.9590157
## 340 1000 0.77456801 1.6518558 1.0363112 1.3571783
## 341 1000 0.75857493 1.3512833 0.8881823 1.1254614
## 342 1000 0.44506328 1.0171609 0.3667804 0.4749483
## 343 1000 0.41738492 0.9855448 0.4812017 0.6726519
## 344 1000 1.45939036 2.9988119 1.6062469 1.5224219
## 345 1000 0.83774810 1.8076014 0.9162327 1.1516865
## 346 1000 0.51862106 1.1618173 0.5526683 0.6548099
## 347 1000 2.02432204 3.6805777 1.8939540 2.2850581
## 348 1000 0.76892229 1.5959039 0.6395406 0.6553072
## 349 1000 1.26485678 2.5937199 1.3213186 1.1519331
## 350 1000 1.71369108 3.4315471 1.6502370 1.5971953
## 351 1000 0.69553486 1.3236985 0.6907322 0.7051401
## 352 1000 0.42921998 0.7607086 0.3966715 0.4893005
## 353 1000 0.45063805 0.9581093 0.3984159 0.4171627
## 354 1000 0.23318347 0.5252685 0.2126675 0.2115251
## 355 1000 1.69573991 3.6403798 1.5272010 1.5873480
## 356 1000 1.08532724 2.0743513 1.0434534 0.9178319
## 357 1000 0.62934933 1.3713426 0.6093862 0.5494967
## 358 1000 0.77913026 1.7681964 0.6336972 0.9996820
## 359 1000 1.81517145 3.6407613 1.8113539 1.7999011
## 360 1000 1.32102145 2.4967540 1.3766158 1.2098328
## 361 1000 0.97959943 2.0464324 1.2038981 1.4401697
## 362 1000 0.98327236 1.5852258 1.1635032 1.5811939
## 363 1000 0.33044404 0.6868657 0.3027431 0.3399862
## 364 1000 1.18991768 2.4081410 0.9686432 0.8971181
## 365 1000 0.56366524 0.9695366 0.6708978 0.9581499
## 366 1000 0.96986116 2.2233512 0.7535522 1.1426486
## 367 1000 1.16180376 2.7457646 0.9761437 1.5331238
## 368 1000 0.96907127 1.7404713 1.1683259 1.3513934
## 369 1000 0.36965655 0.5911555 0.4763954 0.6610746
## 370 1000 0.96379211 1.7016367 0.9011052 1.0891660
## 371 1000 0.99120960 1.8384721 1.1907052 1.3510773
## 372 1000 0.87140742 2.0118004 0.7762590 0.9650639
## 373 1000 0.70485704 1.4399746 0.6479338 0.6292057
## 374 1000 0.39781558 0.9290228 0.3621998 0.4468894
## 375 1000 1.21155664 2.3974297 1.0990691 1.2757657
## 376 1000 0.68951440 1.5861779 0.7191308 0.8079799
## 377 1000 0.53312040 1.2156008 0.5416522 0.5160568
## 378 1000 1.11409952 2.0722439 1.1163972 1.1232901
## 379 1000 0.49263970 0.9434256 0.5414588 0.4856434
## 380 1000 0.55954878 1.2310492 0.6414575 0.8871838
## 381 1000 0.46594441 0.9067635 0.3973943 0.5287578
## 382 1000 0.86087519 1.7947974 1.1402033 1.3737661
## 383 1000 1.76342852 3.6149500 1.7519113 1.7173597
## 384 1000 1.76582549 3.4256412 1.5445461 2.0308499
## 385 1000 0.33662919 0.5958745 0.4026542 0.5300890
## 386 1000 1.09783017 2.3352693 1.1920692 1.3938802
## 387 1000 0.27702993 0.5376063 0.2985354 0.2789070
## 388 1000 0.79357796 1.6028018 0.9493853 0.7544632
## 389 1000 1.39451397 2.7448652 1.4102654 1.3630111
## 390 1000 0.64618816 1.1853957 0.5735699 0.7914248
## 391 1000 0.83291824 1.6045753 0.8524115 0.7939318
## 392 1000 0.99126525 1.7428177 0.8289685 1.2755913
## 393 1000 0.57035739 1.1984508 0.6036874 0.7036773
## 394 1000 1.10042813 2.2405601 1.2081466 1.1886009
## 395 1000 2.26748073 4.3269724 1.9998643 2.7874534
## 396 1000 0.83845737 1.5184520 0.8842307 1.0185831
## 397 1000 0.93969852 1.7235504 1.1295427 1.0600907
## 398 1000 1.14529590 2.0076897 1.3450045 1.1078037
## 399 1000 0.62516545 1.4816354 0.5560560 0.7633844
## 400 1000 0.49780637 0.9521830 0.5441575 0.4819341
## 401 1000 0.19724530 0.3225129 0.2356752 0.3509647
## 402 1000 0.48483006 0.7602858 0.5346857 0.6842525
## 403 1000 0.22485841 0.4135030 0.2670091 0.2186252
## 404 1000 0.94014788 2.0555701 1.0497216 1.3784426
## 405 1000 0.19472812 0.2969285 0.2600449 0.4049785
## 406 1000 1.57571137 3.0136782 1.8077802 1.9200726
## 407 1000 1.24611699 2.6666419 1.3251977 1.5624400
## 408 1000 0.70420648 1.3623950 0.7131782 0.6862630
## 409 1000 0.31722467 0.7258016 0.4011970 0.6531140
## 410 1000 0.80379110 1.4192777 0.8966329 0.7616770
## 411 1000 1.84837340 3.8756128 1.6908030 1.9803975
## 412 1000 0.46437660 0.9188632 0.4142488 0.4891015
## 413 1000 0.69466655 1.2902108 0.9117770 0.9424723
## 414 1000 0.41512845 0.8604456 0.3706258 0.3535286
## 415 1000 0.95305727 1.9121518 0.8437675 0.9379642
## 416 1000 0.62531562 1.2006064 0.5778949 0.6788189
## 417 1000 0.74008774 1.6358005 0.9412848 1.2073234
## 418 1000 0.53703287 1.0510119 0.5711707 0.5476740
## 419 1000 0.82171107 1.7357453 0.7574011 0.9238991
## 420 1000 0.56466027 1.1299986 0.5347027 0.5064403
## 421 1000 0.49814646 1.1227673 0.6954998 1.1172827
## 422 1000 0.76966354 1.3717593 0.7730881 0.7833616
## 423 1000 0.90500578 1.7265448 1.2103339 1.1839516
## 424 1000 1.17667163 1.9005462 1.2921314 1.5808788
## 425 1000 0.57993816 1.1607231 0.6181145 0.5835279
## 426 1000 0.42891447 0.6850299 0.4964999 0.6506197
## 427 1000 0.64681162 1.3540742 0.7229730 0.9502618
## 428 1000 0.73648988 1.7182577 0.6762500 0.8569697
## 429 1000 0.58229425 1.0943649 0.5327862 0.6790126
## 430 1000 1.14458626 1.9594262 1.2516126 1.2413933
## 431 1000 0.70082119 1.5061913 0.6230700 0.8066911
## 432 1000 0.57025083 1.0998740 0.5970920 0.6718199
## 433 1000 0.75543126 1.5265474 0.8722634 1.0283078
## 434 1000 1.01325473 2.2462956 0.9525838 1.1345967
## 435 1000 1.61577447 3.0352140 1.5534836 1.7403563
## 436 1000 2.28445615 4.9470048 2.2485553 2.3562579
## 437 1000 0.97591436 1.9676072 0.8816371 0.9364682
## 438 1000 0.67568086 1.3432057 0.5801506 0.5164462
## 439 1000 1.08468447 1.9704047 1.0748232 1.1044069
## 440 1000 1.78154450 3.2586599 1.6151812 2.1142710
## 441 1000 1.00434858 2.0205466 0.7697397 0.9747250
## 442 1000 0.58384234 1.0943676 0.6431844 0.5192337
## 443 1000 1.48795154 3.1079526 1.3218839 1.4859402
## 444 1000 0.29859547 0.5344740 0.3614106 0.3708785
## 445 1000 0.72758283 1.1489179 0.9928355 1.3704465
## 446 1000 0.47661935 0.9681676 0.4390621 0.4388273
## 447 1000 1.90129765 3.0794800 2.1713174 2.7009195
## 448 1000 1.37381769 3.1116025 1.1558374 1.5876607
## 449 1000 0.87373268 1.3003018 1.1778966 1.9916415
## 450 1000 0.49171898 0.7591113 0.5553794 0.7463607
## 451 1000 0.33241547 0.5036037 0.3764259 0.5084571
## 452 1000 1.46907588 3.1730118 1.2806227 1.1572434
## 453 1000 0.67485503 1.3940987 0.9421536 1.3204238
## 454 1000 0.56438780 1.0302068 0.4418509 0.7489691
## 455 1000 0.68836937 1.2123611 0.6795500 0.6530919
## 456 1000 1.67057015 3.0682078 1.3396164 2.3324776
## 457 1000 2.02619259 4.3187591 1.9630227 2.1525323
## 458 1000 1.12391836 2.4348446 1.1425845 1.0865861
## 459 1000 0.55564724 1.0076922 0.5168609 0.6332199
## 460 1000 0.80878070 1.5435130 0.7283025 0.5934151
## 461 1000 1.33459956 2.7759454 1.4449976 1.7761917
## 462 1000 0.93880072 1.7447680 0.9896211 1.1420820
## 463 1000 1.42093336 3.1416805 1.7872991 2.8863965
## 464 1000 1.15891212 2.3598838 1.1180515 1.1823398
## 465 1000 0.70134267 1.4432746 0.8816357 1.0861755
## 466 1000 0.57192506 0.9355779 0.6103827 0.7257558
## 467 1000 0.17467561 0.3332020 0.1944174 0.2150486
## 468 1000 0.32105322 0.6841842 0.3110888 0.2811954
## 469 1000 2.68189324 5.9285451 2.3744876 2.7483919
## 470 1000 1.39522952 2.6796773 1.1341655 1.5809412
## 471 1000 1.38587303 2.8440737 1.4321812 1.5711058
## 472 1000 0.22691205 0.3659432 0.2821991 0.4466143
## 473 1000 0.81077981 1.6099786 0.7235976 0.8397324
## 474 1000 0.95120465 1.7264158 0.9505022 0.9483949
## 475 1000 1.13136750 2.2660063 1.1933739 1.2635585
## 476 1000 0.83026077 1.9373635 0.7084523 1.0738777
## 477 1000 0.52378218 0.9820272 0.4559996 0.4800100
## 478 1000 0.92842827 1.8199509 0.9130234 0.9592379
## 479 1000 1.58540129 2.9544137 1.3760980 1.4783301
## 480 1000 0.47734935 0.9419028 0.4866109 0.4638827
## 481 1000 0.46312142 0.8508308 0.5774534 0.6516514
## 482 1000 0.73371781 1.2716066 0.8245305 0.7028990
## 483 1000 0.86319365 1.7424735 1.0540662 1.2851543
## 484 1000 2.17010122 5.0471898 1.8121459 2.7664699
## 485 1000 1.23718234 2.2960076 1.1572355 1.3970761
## 486 1000 0.61733952 1.2620125 0.7307539 0.8609102
## 487 1000 1.70150510 3.5200754 1.8774479 2.3460539
## 488 1000 0.31999900 0.6401875 0.4049262 0.4863096
## 489 1000 1.69056478 3.0771800 1.9020652 2.4504387
## 490 1000 0.96183070 1.9644475 0.8886986 0.9175316
## 491 1000 0.26436426 0.4880980 0.3027423 0.3659405
## 492 1000 0.53447718 0.9237062 0.6013159 0.8018320
## 493 1000 0.83717109 1.5685012 0.6737613 1.0969714
## 494 1000 0.57001669 1.0891575 0.6800015 0.6972063
## 495 1000 0.81595568 1.8327793 0.6745438 1.0353018
## 496 1000 0.52758080 1.0823936 0.4801449 0.4595009
## 497 1000 0.90022037 1.8194320 0.7857513 0.7187604
## 498 1000 1.08749500 1.8045781 1.3457744 1.5487571
## 499 1000 0.41790953 0.9657149 0.3691053 0.5155180
## 500 1000 1.14469580 2.1902119 0.9613287 1.2078312
## 501 1000 0.90802031 2.0520799 0.8350245 1.0540120
## 502 1000 0.34637414 0.7404943 0.3479778 0.3431668
## 503 1000 1.24118019 2.5953306 1.1280383 1.2973220
## 504 1000 1.41704439 2.8139917 1.2274708 1.4672872
## 505 1000 1.41581107 2.3266873 1.8419822 2.5291945
## 506 1000 1.26484992 2.7196573 1.0480834 1.2665819
## 507 1000 1.20313603 2.2919649 1.0380378 1.4889038
## 508 1000 1.17252515 2.4536940 1.5002354 2.0995550
## 509 1000 0.84882473 1.4636374 0.9779391 1.2251953
## 510 1000 0.72462707 1.3356656 1.0017852 1.0085983
## 511 1000 1.11396750 2.0665598 1.2050993 1.2655208
## 512 1000 1.14231033 2.2315689 1.1436661 1.1477334
## 513 1000 0.27686147 0.6428091 0.2340486 0.3624872
## 514 1000 0.53458146 1.1879327 0.4511567 0.6646565
## 515 1000 1.44272204 2.7891383 1.4919858 1.3441945
## 516 1000 0.39400959 0.8082594 0.4463672 0.5493253
## 517 1000 1.04585043 1.8076497 0.9821913 1.1731686
## 518 1000 0.31517499 0.5070145 0.3545136 0.4678402
## 519 1000 0.53888587 1.1352153 0.6675920 0.7251862
## 520 1000 2.68440228 5.6034867 2.3860297 2.1535649
## 521 1000 1.07880450 2.4903646 1.1337018 1.1384734
## 522 1000 0.89222397 1.7232106 0.7988758 1.0453173
## 523 1000 0.66872425 1.2582784 0.7648714 0.8582633
## 524 1000 0.85457244 1.8993555 1.0131865 1.4890286
## 525 1000 0.58806026 1.0469864 0.5325429 0.6990950
## 526 1000 1.12160792 2.5057494 1.1308658 1.1030922
## 527 1000 1.77437974 3.3879521 1.5040388 2.1763982
## 528 1000 0.88836348 1.7843248 1.2211248 1.4101119
## 529 1000 1.75585121 3.6618569 1.4006299 1.3804650
## 530 1000 1.13397055 2.3214879 1.3097811 1.6194586
## 531 1000 0.95365372 1.7707373 1.0689829 0.8428866
## 532 1000 0.77667618 1.5784958 0.8322361 0.7138175
## 533 1000 2.29998306 4.6355587 1.9143431 2.2110016
## 534 1000 0.32932554 0.6827448 0.3085117 0.3479321
## 535 1000 1.66276785 2.5627057 1.9427780 2.7828084
## 536 1000 0.43303685 0.8014703 0.3771226 0.4086892
## 537 1000 1.88975324 3.6108935 1.9933012 2.3039450
## 538 1000 1.55246135 2.9074078 1.3613292 1.9347256
## 539 1000 2.00094450 4.0354914 1.8693643 1.8217902
## 540 1000 0.25799426 0.5775261 0.2220398 0.2651573
## 541 1000 1.58359575 2.5838418 1.8186970 2.0562029
## 542 1000 1.01491319 2.1871919 0.9358960 0.7018565
## 543 1000 0.95333503 1.8815971 1.1135496 1.1549749
## 544 1000 0.53310307 0.9952181 0.5056612 0.5879868
## 545 1000 1.84347394 3.4388106 1.5745272 2.3813674
## 546 1000 0.54400278 1.1512584 0.4470621 0.5082534
## 547 1000 0.84830592 1.8257438 0.9345050 1.1931023
## 548 1000 1.79146762 3.7096982 1.6285400 1.7825197
## 549 1000 1.13084798 2.5188315 0.9389852 1.3878947
## 550 1000 0.65075867 1.3595303 0.5976794 0.6896324
## 551 1000 0.69535615 1.2790318 0.7508370 0.9172795
## 552 1000 0.97567356 1.9087528 1.0414595 1.0007597
## 553 1000 0.98567383 2.1237691 0.7943601 0.9121262
## 554 1000 0.66177263 1.2762556 0.6264265 0.7324649
## 555 1000 1.32511563 2.6814147 1.3723219 1.2471571
## 556 1000 1.05873415 2.2910076 1.2655338 1.6192072
## 557 1000 0.98869075 1.7497562 1.1822664 1.4978113
## 558 1000 0.93957797 1.6089082 0.9189336 0.9808667
## 559 1000 0.33646701 0.7674960 0.4112048 0.5946364
## 560 1000 0.84171058 1.8355303 0.7149149 0.7711827
## 561 1000 1.28325310 2.7392746 1.2666442 1.2168176
## 562 1000 0.66206597 1.2022699 0.7739724 0.9311251
## 563 1000 0.73005107 1.1670405 0.8636011 1.0896292
## 564 1000 0.98523980 1.9361074 0.8864911 1.0711702
## 565 1000 0.88750960 1.5856918 0.8987666 0.8649956
## 566 1000 3.08710861 6.5905749 2.7228909 2.1902199
## 567 1000 0.32284860 0.6186276 0.3439256 0.3280754
## 568 1000 0.76596500 1.5645994 0.8644953 0.6984821
## 569 1000 0.77094682 1.6958293 0.7073417 0.6965574
## 570 1000 0.71037537 1.4060949 0.6350411 0.7470149
## 571 1000 1.03678608 1.8530441 1.2549215 1.5881063
## 572 1000 1.40809104 2.9105871 1.5669603 1.6573465
## 573 1000 2.59679250 5.3753492 2.0710642 2.1423819
## 574 1000 1.26925808 2.6592231 1.2467946 1.1794041
## 575 1000 0.40811334 0.9332926 0.5375688 0.9135284
## 576 1000 0.84786052 1.7203125 0.7172415 0.6786145
## 577 1000 1.21082091 1.9944404 1.3561868 1.7169904
## 578 1000 1.30902963 2.8271104 1.2828198 1.3614492
## 579 1000 0.65817288 1.1649443 0.7213867 0.9110284
## 580 1000 1.31312621 2.5043376 1.2734787 1.1545360
## 581 1000 0.75706687 1.4921836 0.9064261 0.8119422
## 582 1000 0.70773425 1.4644601 0.7105734 0.7190910
## 583 1000 0.42353714 0.7148967 0.4583046 0.4952933
## 584 1000 0.18734652 0.3773776 0.2234203 0.2662056
## 585 1000 2.24142140 4.5674307 2.1812698 2.3007530
## 586 1000 1.71130258 3.0648129 1.6251083 1.3665255
## 587 1000 0.80956005 1.8525332 0.6694406 0.9944660
## 588 1000 1.67056858 3.3829874 1.3169515 1.5659429
## 589 1000 0.58984084 1.1766657 0.4556166 0.5973808
## 590 1000 0.55516768 1.0259001 0.5486047 0.5682935
## 591 1000 0.59050540 1.1917861 0.6166299 0.5635673
## 592 1000 0.33411858 0.7275808 0.3414968 0.3636314
## 593 1000 0.58717037 1.0437105 0.5923180 0.6077609
## 594 1000 0.40915409 0.7868230 0.3683174 0.4878671
## 595 1000 1.16859583 2.2559753 1.4123751 1.3716367
## 596 1000 0.34577047 0.7372442 0.3075969 0.3836814
## 597 1000 2.22184374 5.1804332 2.0074658 2.6505995
## 598 1000 0.83424702 1.5906080 0.8201009 0.8625392
## 599 1000 1.99308277 3.6196595 1.7704788 2.1502257
## 600 1000 0.33658033 0.6015422 0.3686422 0.3060016
## 601 1000 1.37254408 2.4849033 1.2081444 1.3155138
## 602 1000 0.57482661 0.9610123 0.7083494 1.0464290
## 603 1000 0.64172861 1.0975847 0.7147107 0.9336572
## 604 1000 0.69625001 1.2679129 0.5817994 0.9251512
## 605 1000 1.91598453 3.9012396 2.2781822 2.8135562
## 606 1000 1.17942204 2.2748768 1.0442885 0.8906828
## 607 1000 0.20676840 0.3668056 0.1981627 0.2239797
## 608 1000 0.31517854 0.5836941 0.3721354 0.3523849
## 609 1000 1.25202313 2.5487796 1.1391627 1.1401899
## 610 1000 1.09427918 2.2235247 0.9732654 0.9396675
## 611 1000 0.66481198 1.4106072 0.8097633 1.0670169
## 612 1000 0.95986350 1.7380515 0.8712654 1.1370597
## 613 1000 0.51471990 1.0530065 0.6685809 0.6762022
## 614 1000 0.85027416 1.8896711 0.8152581 0.9203063
## 615 1000 0.55176918 0.9998538 0.5210231 0.4865400
## 616 1000 0.72251896 1.4341951 0.9224707 1.0953153
## 617 1000 0.85642765 1.9013750 0.7324239 0.7809323
## 618 1000 1.07630580 1.9269526 1.2142773 1.1402124
## 619 1000 1.15417331 2.4282619 1.0731639 1.2919427
## 620 1000 0.39036716 0.8068879 0.3078596 0.3249832
## 621 1000 0.69601036 1.1565609 0.7903317 0.9367565
## 622 1000 0.59290844 1.1154479 0.6596023 0.5503738
## 623 1000 0.87373764 1.6818255 0.8518820 0.9174489
## 624 1000 0.98123321 1.9636583 1.2998442 1.6214347
## 625 1000 1.20321766 2.2871173 1.2026146 1.2008055
## 626 1000 0.63520715 1.3162735 0.5295861 0.5267214
## 627 1000 0.44333922 0.9235382 0.4202781 0.4893664
## 628 1000 1.31787778 3.0439516 1.4656338 1.9089019
## 629 1000 1.80557696 3.6403687 1.5216770 1.4860776
## 630 1000 0.42959591 0.8687912 0.5785386 0.6850547
## 631 1000 1.24656943 2.6996392 1.0861382 1.4419577
## 632 1000 0.49764041 0.7756494 0.6412245 0.9644748
## 633 1000 0.50410998 1.0789232 0.5842562 0.7725155
## 634 1000 0.31293421 0.6082387 0.2705124 0.3439524
## 635 1000 0.70044519 1.4128988 0.6276398 0.6704242
## 636 1000 0.58253869 0.7748301 0.8673226 1.5500817
## 637 1000 0.65069390 1.2567934 0.7209883 0.7621799
## 638 1000 1.25945768 2.5697610 1.0156330 1.1189168
## 639 1000 1.63481238 3.3716643 1.2716607 1.3040240
## 640 1000 0.47437778 0.9200108 0.4777378 0.4676577
## 641 1000 0.27212178 0.5120038 0.3779394 0.3670861
## 642 1000 0.51864565 1.1495263 0.5883820 0.7975911
## 643 1000 0.40979287 0.5907029 0.5086320 0.8051495
## 644 1000 0.50163009 0.8444956 0.5419233 0.6628027
## 645 1000 0.62550775 1.2962393 0.5970966 0.5124483
## 646 1000 0.37741427 0.7690598 0.4496192 0.5574024
## 647 1000 0.58090484 1.1348629 0.5748601 0.5929944
## 648 1000 0.50090227 0.9720642 0.4535775 0.5752531
## 649 1000 0.38800050 0.8492675 0.3155687 0.3731708
## 650 1000 1.04720158 2.1045304 1.0322553 1.0426271
## 651 1000 0.52023574 0.9528963 0.4210247 0.6390977
## 652 1000 0.58149194 0.9891381 0.6663639 0.9119717
## 653 1000 2.04638924 3.8284138 1.9570739 2.2250200
## 654 1000 1.85182156 4.1544553 1.5877663 1.9892942
## 655 1000 1.19654408 2.6597693 1.0375210 1.5145902
## 656 1000 1.01439825 1.9562534 1.1222018 1.0486476
## 657 1000 1.50902047 3.0681461 1.2455542 1.1329723
## 658 1000 0.99008957 1.4379434 1.3728706 2.1614712
## 659 1000 1.82592134 3.9234806 1.4576440 1.7684616
## 660 1000 0.45120133 0.8222107 0.4319416 0.4151057
## 661 1000 1.16487503 2.2687934 1.1477211 1.0962595
## 662 1000 1.46225591 2.8142448 1.5627784 1.7379235
## 663 1000 0.42980653 0.9385426 0.4134675 0.4624846
## 664 1000 0.76464111 1.6773765 0.6853115 0.9233002
## 665 1000 0.94433027 1.9074596 0.8450128 0.8973326
## 666 1000 0.42543414 0.7462212 0.3874761 0.4670270
## 667 1000 0.55337537 0.9551038 0.6175618 0.7212542
## 668 1000 1.86173986 4.2356055 1.5521637 2.4808921
## 669 1000 1.25936450 2.2391379 1.5631527 1.9583423
## 670 1000 0.27449773 0.6177179 0.3418530 0.5439187
## 671 1000 0.57404846 1.1699022 0.6675955 0.7884153
## 672 1000 1.01700651 1.9641028 0.9305260 1.1899675
## 673 1000 1.07860018 2.2441072 0.9955757 1.1298184
## 674 1000 1.93956974 3.9133481 1.6403760 1.8540483
## 675 1000 0.97449647 1.9446162 0.9066405 0.8278427
## 676 1000 1.14466627 2.2648244 1.0685526 0.9311685
## 677 1000 1.95175352 3.6890148 1.8158600 2.2235405
## 678 1000 0.48832691 0.7531777 0.6573229 1.0470171
## 679 1000 1.31639835 2.8877865 1.0733336 1.1431781
## 680 1000 0.38638037 0.6750320 0.4425748 0.4132524
## 681 1000 0.87481862 1.6994246 0.8430125 0.9384310
## 682 1000 1.43041142 2.7209669 1.2783074 1.7346195
## 683 1000 0.41004624 0.8047775 0.4204630 0.3925922
## 684 1000 0.21562976 0.4221919 0.2776590 0.3170192
## 685 1000 1.07086399 2.1381096 0.9542702 1.0799100
## 686 1000 0.31845717 0.5368257 0.3564828 0.3512260
## 687 1000 1.29676074 2.4586953 1.3237775 1.2427272
## 688 1000 0.66827846 1.1135454 0.6889197 0.6269959
## 689 1000 0.83709352 1.8822905 0.7393343 1.0326120
## 690 1000 0.83615327 1.9733772 0.8017867 0.8643603
## 691 1000 0.46600466 0.8868444 0.4906637 0.4166867
## 692 1000 0.99999833 1.7530177 0.8471211 1.3057527
## 693 1000 0.26089752 0.4247395 0.3034945 0.4312855
## 694 1000 1.38243448 2.9101768 1.3120910 1.5231215
## 695 1000 1.07461393 2.0967550 1.0072609 0.8087257
## 696 1000 0.77382529 1.6583172 0.8359660 0.6495438
## 697 1000 0.77399826 1.6911253 0.7932615 0.7354717
## 698 1000 1.09478400 2.3000422 1.1171275 1.1840483
## 699 1000 2.19838357 4.0354628 1.7754369 2.7882140
## 700 1000 0.60429792 1.1709135 0.7111312 0.7237587
## 701 1000 0.58804417 1.1801681 0.5709563 0.5640679
## 702 1000 1.27109981 2.8574063 1.4892487 1.7741453
## 703 1000 0.84657091 1.5479192 0.9181335 1.0452280
## 704 1000 0.49396461 0.9086207 0.5809174 0.4695990
## 705 1000 0.80795462 1.6459521 0.8088999 0.8060640
## 706 1000 0.43070415 0.7173533 0.4446973 0.4740549
## 707 1000 0.91694799 1.7162341 1.2187487 1.2263945
## 708 1000 0.34607796 0.7220653 0.3007074 0.2713046
## 709 1000 0.69234546 1.3364577 0.6533207 0.5520620
## 710 1000 1.12824805 2.5955533 1.5778560 2.8751069
## 711 1000 1.49014712 2.6940487 1.4031695 1.2953467
## 712 1000 0.78697830 1.6372540 0.8820352 1.1353356
## 713 1000 0.40308259 0.8408039 0.4011008 0.3951554
## 714 1000 1.15365495 2.6226548 1.0380522 1.0574060
## 715 1000 1.06136182 2.3065612 0.8651575 0.9925182
## 716 1000 1.13410277 2.0892649 1.0410792 1.3201499
## 717 1000 0.82502516 1.8080066 0.8858441 0.7033873
## 718 1000 0.85718348 1.9113535 0.7281457 0.8793620
## 719 1000 1.29445806 2.8068511 1.0914609 1.4333012
## 720 1000 1.38273892 2.8485112 1.2492336 1.1751555
## 721 1000 1.31617770 2.9881831 1.1756580 1.5972170
## 722 1000 0.88426169 1.5852240 0.7800203 1.0927444
## 723 1000 0.75899139 1.5535496 0.9746913 1.0879147
## 724 1000 1.05561504 2.2979019 0.8791376 1.1693396
## 725 1000 0.70145745 1.4315329 0.6954893 0.7104321
## 726 1000 0.45421147 0.9243692 0.4359476 0.4575493
## 727 1000 1.63046511 3.2522603 1.2947856 1.6521399
## 728 1000 0.43798881 0.9558841 0.3691690 0.4302892
## 729 1000 2.37261192 4.4163127 2.1206635 2.8765087
## 730 1000 0.84885599 1.5285384 0.9255213 1.1555172
## 731 1000 0.85472232 1.8138524 0.7817054 0.9697078
## 732 1000 1.60957636 3.2877442 1.5388130 1.6395283
## 733 1000 1.37935932 2.5335076 1.4194519 1.2991743
## 734 1000 1.61726060 3.0818217 1.4750777 1.9016265
## 735 1000 0.76429617 1.5762170 0.7702220 0.7524446
## 736 1000 1.05804425 2.0545255 1.0849093 1.0043141
## 737 1000 0.22142111 0.3234977 0.2758675 0.4392066
## 738 1000 1.77126264 3.0941179 1.9336194 2.4206895
## 739 1000 1.02304778 2.0104148 1.0388296 1.0861749
## 740 1000 0.79720264 1.3442100 0.9543819 1.1767139
## 741 1000 1.15928433 2.3121770 1.1902568 1.1752634
## 742 1000 1.30755214 2.5275439 1.0569006 1.4409848
## 743 1000 0.34828800 0.6744970 0.3470968 0.3506703
## 744 1000 0.81179297 1.6333166 1.0968406 1.3001195
## 745 1000 1.29185532 2.7544316 1.4879938 2.0764091
## 746 1000 0.59874475 0.9852120 0.6151045 0.6564218
## 747 1000 1.14580179 2.2914785 1.0838517 1.0215890
## 748 1000 0.86585341 1.7763712 0.7108790 0.6675654
## 749 1000 0.61683443 1.1320513 0.7517016 0.8573877
## 750 1000 1.64611574 3.2250431 1.6842036 1.5699401
## 751 1000 1.50746633 3.0706760 1.2598722 1.2511757
## 752 1000 0.58302938 1.0250184 0.7552842 0.8053712
## 753 1000 0.98890158 2.0465672 0.8568794 0.8967672
## 754 1000 1.30988728 2.5291218 1.2443395 1.3885722
## 755 1000 0.77479057 1.5167762 0.8276673 0.7985315
## 756 1000 1.00164151 2.1273789 1.1821180 1.1958188
## 757 1000 2.24319956 4.4340794 2.4213256 2.4686523
## 758 1000 0.77991622 1.4406786 0.7861511 0.8048557
## 759 1000 0.63665756 1.0511710 0.7414392 0.8918633
## 760 1000 1.19412199 2.5614034 1.1153478 0.8790252
## 761 1000 2.06972573 4.7298378 1.7498567 2.1675382
## 762 1000 0.93819156 2.0402224 1.2135347 1.8522921
## 763 1000 0.89835648 1.7692519 0.8251713 0.9670091
## 764 1000 1.18740507 2.2982758 1.1548656 1.2524840
## 765 1000 0.40330624 0.8908180 0.3186243 0.3842820
## 766 1000 2.92085352 6.1036326 2.2380525 2.2660395
## 767 1000 1.27801930 2.5414788 1.3863094 1.4582001
## 768 1000 0.94061013 1.9218256 0.9997524 1.1604080
## 769 1000 1.24927571 2.3899454 1.0746716 1.5207907
## 770 1000 1.53625975 2.8501949 1.3138628 1.9810537
## 771 1000 0.18031714 0.3755651 0.1690723 0.1951546
## 772 1000 1.57898915 3.2446948 1.5607621 1.5060809
## 773 1000 0.72680110 1.1041326 0.9675157 1.6004750
## 774 1000 0.99311640 2.0816430 1.1418904 1.1415693
## 775 1000 1.20359150 2.1275105 1.4117231 1.9027727
## 776 1000 0.76823431 1.6772440 0.8897628 1.2543483
## 777 1000 0.55715763 1.0657836 0.6076515 0.6784868
## 778 1000 0.64033088 1.2050852 0.5349283 0.6570890
## 779 1000 2.33225349 4.6460671 2.1682746 1.9581961
## 780 1000 0.39211173 0.8081974 0.3560266 0.3321769
## 781 1000 0.72133704 1.4456264 0.8425516 0.8139110
## 782 1000 0.79293091 1.4646655 0.9389755 0.7820294
## 783 1000 1.11782968 2.4416909 1.2731557 1.2114664
## 784 1000 0.68772292 1.5236829 0.6359698 0.7912292
## 785 1000 1.50971277 3.0091106 1.3494905 1.1634808
## 786 1000 0.50659848 0.8889169 0.6404486 0.8172986
## 787 1000 0.41856869 0.7310741 0.5293797 0.5370941
## 788 1000 1.11740872 1.9673930 1.3344215 1.7859697
## 789 1000 1.64827470 3.5131421 1.3750815 1.6433699
## 790 1000 0.95404128 1.6874481 0.9014210 1.0592818
## 791 1000 0.83762708 1.4928893 0.9487673 0.8657837
## 792 1000 0.94023915 2.1303701 1.0014219 1.1386465
## 793 1000 0.77523426 1.5945673 0.7272511 0.7895150
## 794 1000 0.22862053 0.4558925 0.3034715 0.3728992
## 795 1000 0.67948865 1.5502114 0.6073942 0.8236775
## 796 1000 1.77668547 3.2345355 1.9383432 1.4533699
## 797 1000 0.83932113 1.5376376 0.7550270 1.0079094
## 798 1000 0.73654029 1.1857892 0.8446511 1.1689836
## 799 1000 1.26562273 2.2084179 1.2833884 1.3366855
## 800 1000 0.92937736 1.8624059 0.7778942 0.7853250
## 801 1000 0.81173280 1.8462343 0.7469466 0.9413052
## 802 1000 1.40292988 2.7070238 1.2137072 1.6500197
## 803 1000 1.41025100 2.5456969 1.3675079 1.4957372
## 804 1000 0.38184109 0.7232693 0.5678901 0.6512775
## 805 1000 0.31903366 0.7168066 0.2668925 0.3300379
## 806 1000 0.84212740 1.5667835 0.7340754 1.0582313
## 807 1000 1.59086227 3.3011201 1.5361754 1.7002360
## 808 1000 3.08356156 6.3111174 2.6882169 2.7235758
## 809 1000 0.84909538 1.6656843 0.8978805 0.8653994
## 810 1000 1.92773869 3.2035179 1.9465376 2.0029342
## 811 1000 0.47806060 1.1289532 0.3692389 0.6661195
## 812 1000 0.30786698 0.6849532 0.2940797 0.2527178
## 813 1000 0.90452166 2.0745364 0.6956124 1.0839674
## 814 1000 0.67689700 1.5378844 0.6642721 0.6263973
## 815 1000 0.63564307 1.2438278 0.6252902 0.6563488
## 816 1000 0.72978282 1.5732129 0.6802690 0.5317277
## 817 1000 1.15325055 2.2742422 1.1912338 1.1485699
## 818 1000 1.22287308 2.4273206 1.1189684 1.2326868
## 819 1000 0.37324788 0.8295646 0.5022178 0.7771613
## 820 1000 1.66080903 3.4833110 1.8347603 2.3566142
## 821 1000 0.89320578 1.7333655 0.9668927 1.0258209
## 822 1000 1.16750152 2.6870887 1.0822389 1.3211097
## 823 1000 0.76205329 1.6379231 0.7273922 0.6565007
## 824 1000 0.72843068 1.4896189 0.9438554 1.1939133
## 825 1000 1.33389485 2.7109949 1.2301040 1.2343263
## 826 1000 1.86335562 3.5381036 1.8386063 1.8743354
## 827 1000 1.85063084 3.8361096 1.9938436 2.4234819
## 828 1000 1.87024985 3.4910733 1.7353284 2.1400927
## 829 1000 1.26311478 2.0851447 1.5429515 2.2590231
## 830 1000 2.23154980 4.8363755 1.9566117 1.8038825
## 831 1000 0.41354524 0.9112090 0.3525154 0.4790314
## 832 1000 0.63510758 1.2529376 0.5834810 0.4886606
## 833 1000 0.76692506 1.4360272 0.7891491 0.8558211
## 834 1000 0.92204117 1.4516540 0.9741652 1.1165971
## 835 1000 0.94300891 1.9876207 1.0579393 1.4027304
## 836 1000 0.34611415 0.5163575 0.4093770 0.5866525
## 837 1000 2.37555667 4.1255853 2.3453803 2.4359095
## 838 1000 0.67258460 1.4187381 0.6325558 0.7526422
## 839 1000 0.98466564 2.1102587 1.0977485 1.4369970
## 840 1000 1.26475205 2.5054433 1.0977622 1.0197685
## 841 1000 0.32878361 0.6141313 0.3085349 0.2477889
## 842 1000 0.52475786 0.9110679 0.7386341 0.8708774
## 843 1000 1.52582849 2.7169065 1.7033493 2.1108359
## 844 1000 1.10940213 2.3797421 1.0441290 1.2399484
## 845 1000 0.84797786 1.6057454 0.7923376 0.9592584
## 846 1000 1.04801399 1.9667992 0.8663272 1.3710858
## 847 1000 2.81652554 6.0133753 2.4923713 3.1190276
## 848 1000 0.88090962 1.7329914 1.0160872 0.9529792
## 849 1000 1.82642300 3.9068052 1.5590272 1.5881318
## 850 1000 0.39195217 0.7857551 0.3635587 0.3397921
## 851 1000 1.07456104 2.2843175 1.1833783 0.9936317
## 852 1000 0.56697312 1.1835120 0.6532894 0.8635199
## 853 1000 0.96171363 2.0230280 1.3096243 1.9065367
## 854 1000 0.97411514 1.9782503 0.8526341 0.8990651
## 855 1000 1.65902827 3.6686254 1.4830636 1.9608929
## 856 1000 0.72531490 1.6317481 0.6495019 0.6619576
## 857 1000 0.77329839 1.4875690 0.6707192 0.9208679
## 858 1000 0.09008694 0.1865607 0.1085314 0.1429429
## 859 1000 1.25745498 2.1363577 1.3058585 1.4510692
## 860 1000 1.16579240 2.5570900 0.9702255 1.3384214
## 861 1000 0.63185713 1.3142348 0.7852496 0.9973196
## 862 1000 1.72051267 3.8140278 1.3950975 2.0021884
## 863 1000 0.67969738 1.5004683 0.9013075 1.2605182
## 864 1000 0.55069870 1.0598567 0.5673574 0.5173814
## 865 1000 2.10106364 4.8777706 1.7284426 2.6592923
## 866 1000 1.58105287 3.0823940 1.6128134 1.7080949
## 867 1000 1.08056758 1.8044669 1.0344289 1.1728450
## 868 1000 0.64726001 1.5256943 0.7805066 1.1802465
## 869 1000 0.66698798 1.4622402 0.8390890 1.2762115
## 870 1000 0.62267541 1.1042675 0.6116620 0.6447023
## 871 1000 1.78847005 4.0515586 2.2614459 3.1285680
## 872 1000 0.78575409 1.4664102 0.8085059 0.8767614
## 873 1000 0.41251348 0.8769504 0.4905765 0.6984481
## 874 1000 1.07028524 2.3481997 1.0455827 1.1196902
## 875 1000 0.78380727 1.7033228 1.0173840 1.5902315
## 876 1000 0.58272595 1.1504337 0.5935248 0.5667782
## 877 1000 0.50111849 0.9361400 0.4788058 0.5457438
## 878 1000 1.87874915 4.1365491 1.5446539 1.9964157
## 879 1000 0.65257827 1.1843201 0.7357445 0.9546694
## 880 1000 0.83015363 1.2349806 1.0076592 1.5401758
## 881 1000 1.80848227 3.8685096 1.5390492 1.3915008
## 882 1000 0.54918853 0.9150732 0.5992162 0.7492994
## 883 1000 1.66432593 3.7315803 1.3178715 1.9787381
## 884 1000 1.08863205 1.8751454 1.2667941 1.8012803
## 885 1000 0.45848990 0.8997519 0.3765785 0.3996374
## 886 1000 0.80139182 1.2669218 1.0570871 1.3596242
## 887 1000 0.68642901 1.5137969 0.7226609 0.7568290
## 888 1000 0.40916926 0.8913619 0.3453688 0.4641267
## 889 1000 0.84642819 1.3403080 0.9631567 1.3133421
## 890 1000 0.99955709 2.3119766 0.8941108 1.2104496
## 891 1000 0.56975543 1.3166485 0.5321807 0.5446503
## 892 1000 0.35318389 0.6901917 0.3238716 0.3936240
## 893 1000 1.04068543 2.3729666 0.9385839 1.2448885
## 894 1000 0.54445273 0.9784964 0.5984677 0.7605128
## 895 1000 1.36803890 2.7555939 1.0649549 1.3192487
## 896 1000 0.57248510 1.1648826 0.6017254 0.6341561
## 897 1000 0.88324103 1.9115922 0.7892404 0.7829782
## 898 1000 1.06765288 2.4150541 0.8316527 1.2950234
## 899 1000 0.40916153 0.8626888 0.4042040 0.3893314
## 900 1000 1.86949065 3.9090751 1.7679081 2.0726557
## 901 1000 1.15075181 2.5575239 1.2238937 1.4433194
## 902 1000 0.35396924 0.5593836 0.4499565 0.7253565
## 903 1000 0.93363539 2.0167878 0.9027463 0.8100789
## 904 1000 0.78955325 1.8097362 0.6905984 0.9874630
## 905 1000 1.07304172 1.8189890 1.0793503 1.0982760
## 906 1000 0.29884940 0.5996684 0.2972241 0.3005228
## 907 1000 0.85611730 1.7313048 0.7083365 0.8084418
## 908 1000 0.86220154 1.6775036 0.9267610 0.9794501
## 909 1000 1.34321605 2.5475399 1.3855633 1.5126049
## 910 1000 1.20421666 2.5122169 1.2883199 1.0360102
## 911 1000 1.34868032 2.8091915 1.3815886 1.4803134
## 912 1000 1.10989053 2.1407946 1.2281088 1.2692589
## 913 1000 0.50021922 0.9226934 0.6709978 0.6474139
## 914 1000 0.34265338 0.6950252 0.4024767 0.3778799
## 915 1000 0.63392004 1.3052458 0.6886334 0.8368612
## 916 1000 2.08508615 4.4715582 1.8857897 1.4181619
## 917 1000 1.92221985 3.6899005 2.5025129 2.3085679
## 918 1000 0.91056804 1.8679543 0.8264511 0.7935224
## 919 1000 0.45743659 0.6897925 0.5880946 0.8937899
## 920 1000 0.95429986 1.6924724 0.9314048 0.8627194
## 921 1000 0.40684078 0.8582165 0.3827373 0.4550477
## 922 1000 0.80132519 1.6801683 1.0389312 1.4703320
## 923 1000 1.04835440 2.1935424 0.9490059 0.9350553
## 924 1000 0.41880347 0.9646607 0.4758202 0.6257899
## 925 1000 1.88956685 4.0031311 1.7041620 1.4609626
## 926 1000 0.60630069 1.2930046 0.6333466 0.7144844
## 927 1000 0.40387870 0.8845118 0.4225908 0.4787270
## 928 1000 0.41291571 0.8279171 0.4962472 0.4077014
## 929 1000 0.65958954 1.1844364 0.7886149 0.7217505
## 930 1000 0.68675971 1.5691863 0.6349765 0.7520191
## 931 1000 0.54748482 0.9839383 0.5098250 0.6106570
## 932 1000 1.55558352 2.9342113 1.4047542 1.8572421
## 933 1000 0.65887766 1.4103938 0.6861745 0.6042841
## 934 1000 0.19652930 0.3469744 0.1952269 0.1913196
## 935 1000 0.83588652 1.9405321 1.0088973 1.5160545
## 936 1000 1.40056693 2.8074644 1.2663435 1.3847406
## 937 1000 0.43511848 0.9444657 0.4678221 0.3737594
## 938 1000 0.55239116 1.1403019 0.5383173 0.4960955
## 939 1000 1.07186831 2.1765697 0.9120743 0.8343629
## 940 1000 1.09650682 2.0104799 0.9717714 1.1861973
## 941 1000 0.66372354 1.3479392 0.7354392 0.8583853
## 942 1000 0.63412481 1.1141815 0.7454451 1.0192952
## 943 1000 1.26147018 2.3737739 1.3810932 1.1278001
## 944 1000 1.46026720 3.0463829 1.1288967 1.1121475
## 945 1000 0.44174892 0.7706215 0.4589274 0.5104628
## 946 1000 1.03158893 2.2115582 0.8875633 0.9368143
## 947 1000 1.64403236 3.0227748 1.5539887 1.8241197
## 948 1000 2.61561615 5.2526750 2.1445067 1.9987209
## 949 1000 0.50940345 1.0779070 0.4676839 0.5737147
## 950 1000 1.78016804 3.0270992 2.2949759 2.6362524
## 951 1000 0.53871513 1.1570411 0.4872563 0.4001256
## 952 1000 2.97164793 5.8607303 2.5820425 3.1780617
## 953 1000 1.16927940 2.4141009 1.0867553 0.9804241
## 954 1000 1.00210077 2.1656874 0.8252821 1.0206661
## 955 1000 1.04116086 2.3597471 1.0910032 1.0655108
## 956 1000 1.30706194 2.7357529 1.0295607 1.0561321
## 957 1000 0.26696863 0.4953600 0.2917105 0.2200093
## 958 1000 0.91796752 1.7680268 0.9610966 0.8344550
## 959 1000 0.35480556 0.6790306 0.4494665 0.4676762
## 960 1000 1.21385875 2.7692273 1.1643619 1.1428915
## 961 1000 0.69870757 1.5059184 0.7125395 0.7540354
## 962 1000 1.06516913 1.6951064 1.3318948 2.1320720
## 963 1000 0.53714201 1.0398167 0.6036096 0.6233102
## 964 1000 0.32092904 0.5347261 0.3894091 0.5887590
## 965 1000 0.45541484 0.8052099 0.4828753 0.4200088
## 966 1000 1.20943426 2.5878566 1.4386521 1.4563793
## 967 1000 0.71898132 1.5146822 0.7158835 0.7065901
## 968 1000 1.77462711 3.4762797 1.8401979 1.9570635
## 969 1000 1.11925621 1.5262706 1.6138312 2.8968957
## 970 1000 0.51134804 1.0840774 0.3907499 0.4236052
## 971 1000 1.00785838 2.1630829 0.8429883 0.8814855
## 972 1000 0.58401844 1.1418318 0.6588635 0.6681960
## 973 1000 2.03785937 3.9395914 1.9493597 2.2148587
## 974 1000 0.90915474 1.6614953 1.2621212 1.2309664
## 975 1000 1.61722986 3.2007301 1.6783358 1.6551176
## 976 1000 0.65397432 1.5132125 0.7995411 1.2362415
## 977 1000 1.47196847 2.7622614 1.2771705 1.6901862
## 978 1000 1.73174900 3.9336186 1.4528421 1.9068356
## 979 1000 0.61430093 1.2899744 0.6094537 0.6239954
## 980 1000 0.47635911 0.7617094 0.5258284 0.6742364
## 981 1000 0.67065674 1.4531151 0.8470915 1.3030303
## 982 1000 1.10011046 2.0507957 0.9335422 1.4332470
## 983 1000 0.64793031 1.1661495 0.7846819 0.7525319
## 984 1000 0.86291133 1.5430853 1.1378041 1.1444808
## 985 1000 1.69132271 2.9249504 1.7872261 2.0749362
## 986 1000 1.27343294 2.3847622 1.5772568 1.6786921
## 987 1000 0.62761561 1.2630882 0.7023564 0.6079733
## 988 1000 0.89514665 1.8779053 0.9403017 0.8785940
## 989 1000 0.99379319 1.6835598 1.0698564 0.9743145
## 990 1000 1.14823545 2.4779972 1.1887916 1.0671231
## 991 1000 0.65231120 1.4760960 0.7666962 1.1098513
## 992 1000 1.12470356 2.5623772 1.1672791 1.1821814
## 993 1000 0.85136983 1.8203913 0.8172142 0.9196811
## 994 1000 1.13176814 2.2110452 1.0297913 0.7965868
## 995 1000 1.82566546 3.2925062 1.8072887 1.8624190
## 996 1000 1.39809881 2.9366629 1.2906241 1.5343125
## 997 1000 1.45244842 3.3649636 1.2060934 1.6551571
## 998 1000 1.13269863 2.1110945 1.2547481 1.2448812
## 999 1000 0.18829803 0.3612777 0.1558789 0.2265938
## 1000 1000 0.55062124 1.0230713 0.6670808 0.7460492
Comparacion de los diferentes propiedades
Eficiencia
paged_table(eficienceDf, options = NULL)Insesgadez:
paged_table(unbiasedDf, options = NULL)Conclusiones
La mayoria de los estimadores son consistentes por que a medida que se hace un muestreo el o aumenta el numero de datos tiende a infinito el valor converge al valor de theta
se visualiza que θ1 y θ3 estan ligeramente por debajo de la media, θ4 esta ligeramente sesgado y θ2 es cada vez mas sesgado debido a que la media del estimador se aleja del valor de 1