Probability density function of multiple structured Normal inverse Wishart
Source:R/mmsNiWlogpdf.R
mmsNiWlogpdf.RdProbability density function of structured Normal inverse Wishart (sNiW) for multiple inputs, on the log scale.
Arguments
- U_xi
a list of length n of observed mean vectors, each of dimension p
- U_psi
a list of length n of observed skew vectors of dimension p
- U_Sigma
a list of length n of observed covariance matrices, each of dimension p x p
- U_xi0
a list of length K of mean vector parameters for sNiW, each of dimension p
- U_psi0
a list of length K of mean vector parameters for sNiW, each of dimension p
- U_B0
a list of length K of structuring matrix parameters for sNiW, each of dimension 2 x 2
- U_Sigma0
a list of length K of covariance matrix parameters for sNiW, each of dimension p x p
- U_df0
a list of length K of degrees of freedom parameters for sNiW, each of dimension p x p
Examples
hyperG0 <- list()
hyperG0$b_xi <- c(-1.6983129, -0.4819131)
hyperG0$b_psi <- c(-0.0641866, -0.7606068)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 16.951313
hyperG0$D_psi <- 1.255192
hyperG0$nu <- 27.67656
hyperG0$lambda <- matrix(c(2.3397761, -0.3975259,-0.3975259, 1.9601773), ncol=2)
xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:1000){
NNiW <- rNNiW(hyperG0, diagVar=FALSE)
xi_list[[k]] <- NNiW[["xi"]]
psi_list[[k]] <- NNiW[["psi"]]
S_list[[k]] <- NNiW[["S"]]
}
mmsNiWlogpdf(U_xi=xi_list, U_psi=psi_list, U_Sigma=S_list,
U_xi0=list(hyperG0$b_xi), U_psi0=list(hyperG0$b_psi) ,
U_B0=list(diag(c(hyperG0$D_xi, hyperG0$D_psi))) ,
U_Sigma0=list(hyperG0$lambda), U_df0=list(hyperG0$nu))
#> [1] 5.689243280 6.537536114 2.714334471 5.034696016 9.545230504
#> [6] 8.672423475 8.867101426 8.545295598 6.426193216 7.287473763
#> [11] 2.077063419 1.561722587 5.481030064 5.260418479 5.684044760
#> [16] 1.460374983 7.034427789 4.531350472 7.726773164 5.161281596
#> [21] 2.130520102 3.572350076 3.302560490 5.879554359 3.929409719
#> [26] 7.170051757 7.127320746 5.908747521 5.785881828 5.855175117
#> [31] 5.214468182 7.238991407 6.883319261 -0.202295421 9.054414731
#> [36] 6.964188176 0.893865969 5.366851260 5.101558314 7.149961823
#> [41] 6.212421055 4.980959096 3.372033248 6.731682469 1.175910036
#> [46] 7.085495847 1.428996841 8.977171579 6.166102279 4.419235764
#> [51] 6.446948216 5.172116387 6.952369348 7.716214016 3.008014432
#> [56] 2.223314707 7.596897093 3.819820749 3.243957408 3.387562873
#> [61] -2.228709816 7.816328289 4.960886341 6.300793692 6.820644847
#> [66] 5.239343880 7.549238522 7.790165809 6.765079032 2.604068542
#> [71] 8.955957420 3.619437672 7.039035144 7.578706443 -1.318171345
#> [76] 3.286538448 4.656748023 6.345170744 8.877172112 1.449831924
#> [81] 7.409239523 1.482496148 7.337245303 6.182724504 7.994471093
#> [86] 2.505672777 6.107862629 5.634700651 7.786272250 8.124156496
#> [91] 7.185841029 3.187968997 6.840443972 3.256552577 -0.939176223
#> [96] 5.675863232 1.523874977 2.886908977 3.495673486 5.653078318
#> [101] 5.893758533 6.936419004 7.882110653 7.591673154 6.297923741
#> [106] 7.577236392 7.821623698 6.505721299 8.075756849 2.354342979
#> [111] 3.262835332 7.660159495 9.557983322 3.582578213 2.396413362
#> [116] 6.684284323 8.364391650 7.243891327 7.139147714 7.948695477
#> [121] 8.167878262 7.496132994 7.144079477 8.789990148 7.293900460
#> [126] 3.442916348 5.215325922 6.323679218 7.136288595 6.849324618
#> [131] 6.065980870 4.062323097 5.674458409 1.099323827 4.863389470
#> [136] 7.381567218 3.507132356 3.934384090 7.624698293 7.516606155
#> [141] 8.280254644 8.091795192 5.160088669 7.966905543 7.371563791
#> [146] 7.422356429 5.286717218 8.405937875 6.632071004 2.917921506
#> [151] 7.655723650 6.173256171 6.197513415 7.413195969 3.737273420
#> [156] 6.544916450 3.691601486 5.551304095 3.761636428 9.211102341
#> [161] 6.087706226 2.486401945 7.548173394 7.291353399 6.138576779
#> [166] -0.221697429 7.619834754 5.027953429 3.990409032 3.527740062
#> [171] 7.027998490 4.836467126 6.737619566 5.910178797 3.391346319
#> [176] 8.509173587 8.107038542 8.138672420 7.203110521 1.943937338
#> [181] 8.795679900 8.553560301 6.463503142 7.661739578 7.366268106
#> [186] 3.256349507 7.276287236 7.291667721 6.427142250 9.189153851
#> [191] 7.043982717 4.316314521 6.839931314 8.193663521 6.228144634
#> [196] 1.122449679 3.686621839 5.637492094 1.772780215 5.330102645
#> [201] 3.164338072 5.197122608 6.569952955 4.190457232 7.805997200
#> [206] 5.845252326 4.382315796 8.382205609 6.519024293 5.679950676
#> [211] 5.843272600 6.753588737 8.349338614 6.670975491 6.830060275
#> [216] 5.110551159 0.894803963 8.020712992 3.317188348 3.536240203
#> [221] 3.731268300 7.307166737 2.313337760 4.708377171 5.662379368
#> [226] 4.703746407 8.423259521 5.021399916 0.702716654 5.370214039
#> [231] -2.139716296 6.118042919 6.800748280 8.591295209 2.659031173
#> [236] 6.565173930 7.738564980 8.432149013 3.617543061 6.230087138
#> [241] 6.643343019 4.912807994 8.355607104 4.544409384 6.757434370
#> [246] 7.813415597 7.270458578 5.509474501 6.554453258 2.217252732
#> [251] 5.207413530 5.629002096 2.863723369 6.756745337 2.725054679
#> [256] 5.683185421 7.590322534 7.737589908 7.587360501 5.327693719
#> [261] 6.790295433 4.148019922 7.856234954 1.078879224 8.921806835
#> [266] 6.332786705 6.498915154 5.667329070 7.238571517 4.939245212
#> [271] 5.848916277 5.692650104 7.386100366 3.016563992 7.224697873
#> [276] 6.211686061 6.573554941 7.337405464 5.370968446 7.249758966
#> [281] 5.840417731 8.543052701 8.366817101 8.398659265 7.385621433
#> [286] 8.100156586 7.655436982 3.092533278 5.854772341 8.174012089
#> [291] 8.849025652 4.197344032 7.854932693 4.044092656 4.907919256
#> [296] 7.600330991 4.526311984 0.254606989 2.489919408 3.877147388
#> [301] 5.280810028 8.028409634 6.500457258 6.686391158 6.753388654
#> [306] 6.308719816 9.554337388 5.702108722 9.039334338 7.103097103
#> [311] 8.566911483 -0.525488831 8.760537087 7.871736428 2.833330071
#> [316] 6.445477009 9.174788214 6.498066777 7.463600630 7.769685750
#> [321] 0.165797165 6.412940447 4.457652097 1.153889876 6.825231177
#> [326] 3.141823193 7.946565466 4.526503931 4.656322249 6.957952759
#> [331] 1.439347570 5.254980687 6.772682897 5.374747722 7.058085812
#> [336] 4.616354388 6.269616057 7.334524024 3.920750345 7.312034260
#> [341] 5.387172612 6.777076077 8.916543139 8.421333289 5.711057788
#> [346] 7.376638075 6.942248273 4.509641288 7.429615931 8.924939303
#> [351] 3.172611887 5.720875352 5.661573431 7.796671421 5.504805358
#> [356] 6.762641383 2.918179066 7.491256913 4.856566003 6.567825807
#> [361] 1.263517283 2.986281294 6.356226707 4.223916181 5.124053897
#> [366] 7.416081253 7.747399374 4.047724557 4.777735802 6.615414724
#> [371] 4.439296550 3.766112228 4.811589604 8.975459375 8.454758056
#> [376] 1.808495301 1.625308847 4.597488552 8.968167170 6.337860695
#> [381] 6.626589213 7.302943925 6.559766111 8.355344890 3.426207515
#> [386] 5.770642032 0.367566465 4.283104695 0.340234233 6.541332742
#> [391] 7.097097181 7.609325379 7.502126462 4.182359028 7.163204481
#> [396] 4.159226502 5.318664414 6.411585368 8.249683375 3.347274475
#> [401] 8.401826084 8.753792197 3.073620169 3.252322290 5.702591487
#> [406] 6.355489799 6.615650505 7.505194200 1.444098655 3.126735805
#> [411] 6.921388182 7.843396945 6.805538632 5.915302351 3.166617688
#> [416] 5.397399301 7.221579515 7.689827745 0.290746907 6.544188833
#> [421] 7.069537131 5.827078857 6.497975104 6.480786397 -0.152490235
#> [426] 8.334267600 8.576646471 7.785966289 8.726738258 8.297315606
#> [431] 7.760817339 4.283588356 4.413555275 7.530303119 6.164887132
#> [436] 5.928350747 -0.904990782 2.706025671 5.617969260 3.853563809
#> [441] 3.486676215 8.363717060 6.724902309 4.790311908 4.504640307
#> [446] 6.888876349 7.085186344 7.678613861 1.656568323 6.460735180
#> [451] 6.473354731 2.866765500 5.116231206 6.638637189 7.822449909
#> [456] 1.826305345 4.952583964 6.275071192 8.227717458 6.416360316
#> [461] 5.269759707 5.364834395 8.713343093 6.811341953 2.199081449
#> [466] 7.810525430 -0.009389914 7.225538264 3.729472354 6.006223331
#> [471] 3.122615879 7.275909161 5.436091626 6.492824247 3.923832057
#> [476] 5.839573417 3.381002893 6.316209768 9.262214811 7.049953577
#> [481] 5.085727332 7.726361988 4.693540932 9.300627879 5.550219938
#> [486] 3.405555417 9.291213662 4.818048206 3.789720157 6.223069246
#> [491] 9.201759510 8.280455988 4.009637084 1.194725318 7.938349008
#> [496] 7.561978344 3.433920685 2.173174556 6.133695068 7.301467049
#> [501] 7.090016076 8.045700550 4.892394419 7.162669032 2.364426049
#> [506] 5.887971251 3.907544811 6.541506076 7.235655845 8.632867132
#> [511] 7.777197837 6.578937608 7.837656309 5.465287701 2.954927696
#> [516] 3.007010894 8.602758803 2.018923600 4.966433143 7.764380397
#> [521] 8.570071359 3.315064181 2.144667892 4.091162663 5.031027476
#> [526] -0.842998380 7.117157398 5.832338467 6.582508858 4.064905884
#> [531] 8.822909060 5.542772513 6.670500181 6.568421080 6.895059232
#> [536] 8.100553467 2.324390485 3.986745675 8.700207746 7.662654104
#> [541] 7.033065891 4.700837646 8.193036144 4.235572935 4.669748784
#> [546] 5.812173551 6.663092120 8.724990855 2.503613417 5.388924595
#> [551] 1.532710769 8.745389739 5.589845191 3.341119281 5.148491008
#> [556] 2.405634513 7.346800583 6.542627769 5.954268059 2.572505887
#> [561] 2.945381348 3.885954910 8.054548826 6.670166119 6.463405765
#> [566] 0.287251774 4.887878333 3.527537991 8.581924111 5.323341158
#> [571] 6.605768785 6.960762954 6.280036116 1.184873639 2.195522929
#> [576] 7.057933590 5.030246546 3.932741556 8.944845927 4.261583578
#> [581] 2.170595318 3.768420660 8.055821346 7.058012295 7.303270729
#> [586] 5.878905192 -0.200046211 6.565642627 7.758809591 7.081770278
#> [591] 5.239830710 5.457920434 5.093236939 8.046077313 6.586291527
#> [596] 6.589078665 7.069085929 6.491978470 7.637200356 6.964831996
#> [601] 7.296895459 6.690531333 8.822452695 5.386904766 4.667885093
#> [606] 8.443739271 5.069943296 5.395587907 7.522430795 5.220178257
#> [611] 5.740419230 4.672943031 6.296707598 8.593212881 8.409981782
#> [616] 1.734441632 5.620826549 7.318277772 3.300994106 9.390092091
#> [621] -3.224947155 7.195333783 7.110367551 4.419259428 7.606218444
#> [626] 9.137781143 7.618162637 5.403441477 4.762640043 5.206834822
#> [631] 6.245878694 6.601269581 6.801241454 5.879705409 4.400671946
#> [636] 6.968676200 7.812002471 8.398311551 3.331445813 7.160306862
#> [641] 7.980979964 3.031171001 7.752411012 5.403135941 6.549017550
#> [646] 4.019644001 3.942268858 2.183480625 7.881390800 6.872391677
#> [651] 8.217726790 7.239194522 6.764632210 5.020807445 7.458553083
#> [656] 0.131095330 3.983935170 7.688877293 8.949594421 3.560413531
#> [661] 7.609080012 5.770313093 6.164637729 5.738192779 5.142738526
#> [666] 6.026847914 8.207324346 2.806305915 4.522292903 8.212860765
#> [671] 7.230538934 5.298506995 4.534339041 7.081479361 6.362947106
#> [676] 5.264682012 7.230287728 3.347725729 5.631065854 7.353437371
#> [681] 7.639633958 6.288040173 2.430412685 5.951077650 7.397847184
#> [686] 7.807779079 6.175181257 5.603895753 5.412672701 2.605620969
#> [691] 6.187306832 6.139340519 5.314597587 6.468041684 6.814555016
#> [696] 8.476768364 2.471059619 2.863700953 6.556538185 4.606556562
#> [701] 8.215602801 5.658607335 4.749897235 8.032265359 6.189713672
#> [706] 6.698308565 8.132883792 6.969941725 3.339393520 5.262544529
#> [711] 4.688127116 6.173615058 8.400437655 3.835696776 5.495948225
#> [716] 8.567242263 2.226524947 6.376797344 5.179578989 3.966576196
#> [721] 4.934836254 7.289454602 7.616586595 3.761281319 6.997625276
#> [726] 6.880067302 7.269448907 7.715717261 6.248487947 6.621944135
#> [731] 5.657518683 5.074483868 7.027000925 2.055521751 5.947083977
#> [736] 2.969367152 7.950058152 7.527979673 6.879307882 5.053697443
#> [741] 4.503030851 5.253210425 0.341578861 4.729542594 4.643459841
#> [746] 5.863015334 6.943917160 7.829252135 3.865150907 7.839597735
#> [751] 3.737367384 1.902437161 7.609952343 7.005866428 3.686916364
#> [756] 7.627124445 -0.972017034 7.793216706 3.344919742 8.419571344
#> [761] 2.557571480 6.268428081 5.779310735 5.396186186 8.382400552
#> [766] 5.978826884 9.416179573 7.099443941 5.395045533 5.292700784
#> [771] 3.631828312 4.726774656 6.037552461 1.328785401 7.738382588
#> [776] 1.803663755 4.915675063 4.244097944 6.298386072 5.890145877
#> [781] 4.710512361 5.901452822 8.464465932 7.261332932 8.991776974
#> [786] 7.621259515 1.783190173 6.923763205 7.798133827 4.664287579
#> [791] 6.738425627 7.513594388 4.664911709 4.911998513 3.602064465
#> [796] 8.841752022 8.662892989 5.936422236 6.829928989 4.147228440
#> [801] 6.545764162 7.079347136 1.795092211 5.840618500 8.846125706
#> [806] 6.688214370 5.518976807 7.846831496 7.319251609 6.715955764
#> [811] 7.353397768 5.204994006 3.166457546 6.196351988 9.740193764
#> [816] 7.079878664 4.539694681 7.601001160 7.819979943 7.575435823
#> [821] 5.713462323 4.334113379 6.808027414 5.386091589 5.966394219
#> [826] 6.590018511 -1.061036678 8.445350557 3.326821393 7.168574766
#> [831] -0.420953943 6.136652308 8.135528928 5.445872572 3.204211027
#> [836] 6.564066457 3.707001135 8.018003201 4.090803591 2.450436111
#> [841] 0.124356945 8.197853949 3.841965822 8.990024792 8.359341333
#> [846] 2.751729695 4.296897545 1.939889168 6.886409794 7.975770931
#> [851] 7.061346849 6.796059848 4.155972852 5.932596568 6.880463762
#> [856] 5.169356660 5.724478357 7.972296232 6.249440167 6.381612805
#> [861] 3.761382320 3.300213474 7.203821166 7.031051940 4.717042868
#> [866] 6.459426650 4.662230577 1.629117797 3.905843120 4.397055581
#> [871] -4.178393150 6.563841050 6.487052515 5.461131140 6.422169906
#> [876] 4.752114399 6.899667807 7.337628733 4.026215654 6.243098113
#> [881] 4.508995425 6.589483249 5.774583413 6.074448643 4.235056375
#> [886] 5.812689176 7.664294402 7.110329171 4.643317963 8.113416565
#> [891] 7.080867026 5.861173056 1.604480969 7.719142864 6.596932296
#> [896] 6.488295391 7.313131729 6.306480551 5.140074385 7.600005658
#> [901] 5.405405154 4.797453562 0.601362848 5.625301089 3.149922959
#> [906] 6.975310374 7.724045470 0.529508535 7.691883283 8.433785208
#> [911] 5.939551551 5.687634800 7.114004473 1.782721650 5.634711668
#> [916] 4.663935288 3.778150075 9.112858922 8.428542321 6.335321390
#> [921] 4.213324150 7.350717607 4.418541118 6.813474761 8.627154988
#> [926] 5.823820705 7.062835423 7.998192983 8.565247221 5.571113038
#> [931] 5.637800593 9.771050147 3.187446313 4.721353951 6.626176450
#> [936] 7.655561787 1.638110885 5.674338005 7.063351102 4.928752203
#> [941] 8.137402453 7.406527220 6.228311822 4.732998825 4.757473458
#> [946] 7.039897057 2.596888738 0.969921273 6.084516362 5.884689330
#> [951] 7.485446783 5.516912528 4.778680062 8.231666338 7.360048380
#> [956] 2.835863626 2.956819552 5.391018418 6.561743067 6.226253545
#> [961] 8.381079365 3.157036067 6.796582089 6.537255467 6.843261666
#> [966] 4.217904715 6.944115384 7.261031968 8.286322402 0.348250787
#> [971] 3.110753906 5.091804687 2.491682472 -3.950366099 5.489996159
#> [976] -0.307741563 8.932782261 3.158383126 6.248195042 7.644891765
#> [981] 5.743412594 6.394563063 6.132950046 6.588500616 7.792311427
#> [986] 8.638594735 2.780447309 8.980831237 5.053221836 5.416357497
#> [991] 6.799293180 5.489089543 5.807785568 6.059768800 5.896254467
#> [996] 6.333249677 4.789924805 6.663543968 8.425502116 2.977118279
hyperG0 <- list()
hyperG0$b_xi <- c(-1.6983129)
hyperG0$b_psi <- c(-0.0641866)
hyperG0$kappa <- 0.001
hyperG0$D_xi <- 16.951313
hyperG0$D_psi <- 1.255192
hyperG0$nu <- 27.67656
hyperG0$lambda <- matrix(c(2.3397761), ncol=1)
#'xi_list <- list()
psi_list <- list()
S_list <- list()
for(k in 1:1000){
NNiW <- rNNiW(hyperG0, diagVar=FALSE)
xi_list[[k]] <- NNiW[["xi"]]
psi_list[[k]] <- NNiW[["psi"]]
S_list[[k]] <- NNiW[["S"]]
}
mmsNiWlogpdf(U_xi=xi_list, U_psi=psi_list, U_Sigma=S_list,
U_xi0=list(hyperG0$b_xi), U_psi0=list(hyperG0$b_psi) ,
U_B0=list(diag(c(hyperG0$D_xi, hyperG0$D_psi))) ,
U_Sigma0=list(hyperG0$lambda), U_df0=list(hyperG0$nu))
#> [1] 2.871116910 1.164065302 -0.042139274 1.121318232 1.915537613
#> [6] 2.925285942 1.221807810 0.810960656 2.733623832 2.597308858
#> [11] 2.566513407 2.351449274 1.636939915 0.933281745 -0.873135685
#> [16] 2.213076141 2.922419168 0.286284328 -1.596313193 2.023418883
#> [21] 2.556967623 0.432063075 1.981614656 1.507252286 2.799086768
#> [26] 1.566383124 2.390404588 0.142950757 1.056436295 1.956613505
#> [31] 2.448387498 2.058481245 2.806365081 2.526298779 2.674311551
#> [36] 2.516916165 0.664003642 1.981238261 1.141881353 1.664687693
#> [41] 2.898883649 0.528600230 0.625526181 1.218335291 -0.895131441
#> [46] 2.553390854 2.539283862 2.162240748 2.430770424 2.576230098
#> [51] 1.107686091 1.949145209 2.218607929 1.283645147 1.211992018
#> [56] 2.290403285 -1.215908399 2.222638367 -1.259165368 -1.681948932
#> [61] 2.887931686 -0.014509031 1.666032541 0.817387660 2.473254448
#> [66] 2.427785697 0.250093679 2.033748261 1.949802894 1.626906819
#> [71] 1.359001759 0.957598562 2.620321747 2.438952240 0.862169685
#> [76] 2.828681902 1.335888562 0.833140562 0.141761186 0.492625804
#> [81] 2.890428442 0.613442841 0.449974815 -2.232793383 1.198601904
#> [86] 2.005700286 2.626020439 2.812351126 2.079489058 2.422671567
#> [91] 0.427555560 -4.924038473 2.781584362 0.975669234 2.772240161
#> [96] 2.563561184 -0.404859302 1.982259969 2.904904362 -0.951750287
#> [101] 0.998784656 1.489081700 1.444209547 1.357346828 2.351973908
#> [106] -0.736155729 -0.258931364 2.985308345 0.744968513 1.983328943
#> [111] 1.813497092 -2.336983977 -0.531319712 1.313681921 1.650710980
#> [116] 2.691510872 2.785142940 2.794279775 2.022565317 1.861164490
#> [121] -0.455889142 2.150758594 2.288528580 2.246495794 2.309363531
#> [126] 2.263404372 0.880647380 2.403322918 0.659505285 2.247633593
#> [131] 2.588423803 -0.467166787 1.691861932 2.818750791 2.505710317
#> [136] -3.044044032 1.495265981 1.066891672 1.972929116 2.383529160
#> [141] 0.342727172 2.049688674 2.577453909 2.321722928 2.544767234
#> [146] 1.425708460 2.300862946 1.310355137 2.172394204 1.149239745
#> [151] 2.892243951 2.307383556 2.317649369 0.748521088 -0.044366309
#> [156] 2.406257341 2.003843244 1.970450912 -0.090641628 2.602278325
#> [161] 1.618568633 1.403725805 2.335545531 1.978332623 2.504197208
#> [166] 2.219942469 2.138778785 2.717951083 2.658833942 2.254181333
#> [171] 1.505792904 1.380959934 -1.027911115 2.788140053 1.248202145
#> [176] 1.059822855 2.577257398 -0.906218836 1.160891430 0.932238941
#> [181] 0.931541854 2.654215219 -2.043068018 2.209819378 0.996586290
#> [186] 2.569690887 1.797201930 0.327488534 2.326262259 0.431969346
#> [191] 1.912177088 1.124934370 2.280208246 2.534667398 1.967408230
#> [196] 3.010596834 2.980425845 2.641666633 0.090756295 2.282246399
#> [201] 1.598810499 0.291530050 0.216687166 2.065579317 2.028522550
#> [206] 2.531637282 -0.088689898 1.764148273 1.427557665 0.684232672
#> [211] 1.916863733 2.799562104 1.874165985 1.348156869 -0.009556799
#> [216] -0.468242157 2.014417901 1.953169282 2.077700914 2.746577773
#> [221] 2.238718282 2.301456501 -0.299696539 0.364861755 2.943817873
#> [226] 1.763129053 -2.260844626 -3.700777421 1.720405723 2.213535228
#> [231] 1.974151510 -0.364983137 2.395400011 -0.714812862 0.748377231
#> [236] 2.618945889 2.403991946 0.319329520 2.397639350 2.711176317
#> [241] 2.761591575 2.613393900 2.629689191 1.164472977 2.321317273
#> [246] 1.231710790 2.469369017 1.606300275 -0.067291310 0.061436989
#> [251] 1.026718005 2.079862685 1.836286379 1.957146785 -0.835891784
#> [256] 2.944414740 2.216478236 2.694236254 -0.535615607 -0.885773295
#> [261] 2.031934133 0.783638703 -1.022856647 0.792312168 1.879541279
#> [266] 2.260175213 1.336621757 2.451869936 2.168775010 1.071194027
#> [271] 1.017796019 0.500942186 2.110975422 1.640916870 -1.255086578
#> [276] 2.707538882 0.098942585 2.906793215 2.124397794 1.595706552
#> [281] -0.780335951 1.373661812 1.025621098 2.097970242 0.919450114
#> [286] 1.618255881 2.648336558 2.849714034 2.581080324 -0.770702851
#> [291] 2.759568002 0.355562039 1.983239234 -0.116286302 1.580750077
#> [296] 2.049017001 2.411261591 -0.239171474 2.630217474 -2.590913554
#> [301] 2.165772612 -3.893217529 0.229612054 0.284118942 1.997726654
#> [306] 1.195436153 1.631516251 2.806567829 2.542829896 -3.163129889
#> [311] -1.622958899 -2.348831108 1.375629956 0.187795809 2.534822813
#> [316] 2.543450549 1.440374509 1.975156889 -4.049980160 1.979934195
#> [321] 2.300399105 -0.346609223 2.783264496 1.302190562 -2.658992440
#> [326] 1.566325078 0.304456066 2.911218184 2.931791991 1.653001373
#> [331] 2.102999787 1.318857445 0.799480723 2.235093170 1.416420974
#> [336] 0.231064273 1.013942882 1.958711771 1.971163378 2.913448300
#> [341] 1.452877496 -0.060783609 0.301911404 1.732259395 2.069994518
#> [346] -0.715758599 -2.420712656 1.728219252 0.788350635 1.214448896
#> [351] 2.689825936 1.521690667 2.114270210 2.633787353 2.239735070
#> [356] 2.245495595 2.374244857 0.786998565 1.496150439 2.014203488
#> [361] 2.242024606 0.995527815 0.390263573 1.221866673 2.824831028
#> [366] 2.439652404 -4.187539178 2.547968764 0.811682225 2.950327752
#> [371] 1.777440095 1.652882965 1.732990681 0.850156784 0.505860262
#> [376] -1.423252407 2.546729830 -0.721045106 2.689563194 2.626108500
#> [381] 2.327481048 1.970566314 1.320197460 1.617557104 1.331272677
#> [386] 1.803204984 2.304816528 2.739036131 0.741028955 2.059534788
#> [391] 2.753902060 2.565335516 2.113742319 2.654173635 -1.067808909
#> [396] 2.402469463 1.413930941 2.909220111 -0.826158742 -0.616251369
#> [401] 1.443197771 0.797830255 1.159069940 2.756181496 1.538738541
#> [406] 2.663191831 0.738625224 0.858274907 0.375596258 2.671193035
#> [411] 0.102053671 -2.027477363 2.511860847 2.012106898 1.512428923
#> [416] 2.704405327 2.069909475 1.660805976 1.944617961 0.450665521
#> [421] 2.154308104 1.935491108 1.897355752 -1.456168101 2.250162608
#> [426] 2.841547072 0.039480611 0.999433206 -1.171616628 -1.745975594
#> [431] 2.108539433 0.982816399 1.606445710 2.485012662 2.277415139
#> [436] 1.321747456 0.896779677 1.366672329 0.241310374 3.006290116
#> [441] 1.339362434 0.546758139 2.818651280 2.541089951 2.685602797
#> [446] 0.853087338 2.429836354 2.494439744 1.981061456 2.432789634
#> [451] -0.566769431 2.331753924 1.260527742 0.127028348 1.536416508
#> [456] 1.881699889 1.665974150 1.136368162 2.505627749 2.551257478
#> [461] 2.067471353 -0.385941015 0.108092602 -1.325815534 1.651815607
#> [466] 2.153292091 2.045477091 0.304369762 1.870936464 2.573108277
#> [471] 1.527267994 1.817860246 -1.176146986 -0.620993851 -1.641284229
#> [476] -1.155409064 -1.598403234 2.713492668 2.628182398 0.767185436
#> [481] -3.574695278 2.654016952 1.195148913 2.669534976 1.807291965
#> [486] 2.519010196 2.189920490 1.305850329 1.983809595 2.189041564
#> [491] 2.699413565 2.806262179 1.783635430 2.136409669 -1.835842736
#> [496] 2.870433037 1.940838726 2.132418118 1.880406466 1.902934493
#> [501] 0.997427296 2.658652183 1.181091836 2.932100558 1.517775375
#> [506] 1.937994532 1.268451186 0.088057451 1.558451995 2.932131248
#> [511] 1.905716106 1.593768069 -0.424284406 2.331190726 1.943110213
#> [516] 0.875723976 -3.296975173 1.935827494 0.692256928 1.798668404
#> [521] -3.976721436 1.978334865 2.250273834 1.851869354 0.216366035
#> [526] 2.644353257 2.885651084 2.093406192 0.103386091 -1.184438082
#> [531] 2.396905435 1.515158248 0.342545063 0.364098658 1.127579544
#> [536] 2.053946302 1.783671555 -0.963219314 0.113811720 -0.568214589
#> [541] -0.931277016 -0.422131483 1.325371261 2.985955784 2.051911950
#> [546] 2.785304638 0.988363522 0.117343246 -1.051105581 1.586379205
#> [551] -0.028623054 -0.246518558 2.451591311 1.212427478 0.616692880
#> [556] 0.842636693 0.233755375 1.703193424 2.819246887 2.762978666
#> [561] 2.896018571 2.636886020 -4.072731286 2.828082377 1.335286534
#> [566] 1.195144273 2.008904793 1.534507546 3.015971556 -0.260194185
#> [571] 2.426685876 2.589926376 1.267963831 -0.618321031 1.912901129
#> [576] -0.726727911 2.982718939 0.829838458 1.778178856 1.993648640
#> [581] 1.742542672 2.102314555 2.850280310 0.915430848 2.314287846
#> [586] 1.814726190 2.446391389 -1.162911853 1.849525516 2.210040990
#> [591] 1.582469418 1.396827139 1.473477655 -1.345155389 2.149283196
#> [596] 0.660442847 2.680840533 0.937494898 -0.908404179 2.908089730
#> [601] 2.218250730 1.742489058 0.061394006 1.788009092 1.282647175
#> [606] 1.318638576 0.716793856 0.732304494 1.845319546 2.547208646
#> [611] 2.513677491 1.521476463 1.913774825 2.399639513 2.708249139
#> [616] 0.265300397 2.386439865 -0.505018518 1.710299787 1.743076941
#> [621] 0.473939029 2.843623240 2.209322341 2.579813226 2.208744690
#> [626] 1.619151942 2.284539509 1.646452119 0.763689250 2.585342536
#> [631] 2.118141827 1.719622539 1.430170811 2.747705427 2.793723379
#> [636] 1.669184066 1.653171615 -2.472657417 1.866424504 1.455538190
#> [641] 1.058034854 1.846485943 0.431147108 0.999010073 2.447136879
#> [646] 2.361502108 -2.697685300 1.476455497 1.782107693 1.489820985
#> [651] -0.542696233 2.140402007 2.223417471 2.688619849 2.611072311
#> [656] -0.285039170 1.384523196 2.438091544 2.770791297 2.606282998
#> [661] 2.938128232 2.789174981 2.878276299 1.053305559 1.731104970
#> [666] 0.264233168 1.908603911 1.801740404 2.784749364 2.566311764
#> [671] 1.524563485 1.023669030 1.266274090 0.541599723 0.313684092
#> [676] -0.286431528 -0.733750928 -1.740362291 2.693252821 0.556550403
#> [681] 2.479919061 1.481674172 2.261176512 2.780571621 2.189672861
#> [686] 2.116376387 -5.020360333 2.833647997 2.056840163 1.160724083
#> [691] 1.669226601 -0.173962880 1.781808879 -1.904825505 0.299976981
#> [696] 1.661313529 2.471685711 2.411047619 1.587904627 1.607512300
#> [701] 1.525163047 -1.147196930 2.340241451 1.420482883 1.310967278
#> [706] 2.262495792 2.280789341 1.167009882 1.829059219 1.032744848
#> [711] 2.799940623 1.607086689 2.248758388 2.294969767 -0.351524991
#> [716] -4.503359624 1.856251099 1.667162922 1.465520686 2.724032926
#> [721] 2.792429435 2.836053828 1.791367072 2.836994465 1.147403660
#> [726] -2.599373470 1.864594502 1.661909294 0.419500182 1.459303554
#> [731] 2.609266646 2.473300964 -2.629194612 -0.470530225 2.870483772
#> [736] -0.584527818 2.037258681 2.505141546 1.677700958 0.356373470
#> [741] 0.851601840 2.273144252 1.942204835 2.392848071 0.077936233
#> [746] 1.399909621 0.213388920 2.098098531 1.453139195 0.508432822
#> [751] 0.657917491 2.178996755 1.341571733 2.082954864 2.457390926
#> [756] 0.931840779 2.549547575 1.442852258 2.554478042 1.777037533
#> [761] -0.513389935 -2.638645712 1.926680908 2.331000525 2.680610858
#> [766] 1.516520214 2.361923692 2.987144547 1.410371655 -1.651671185
#> [771] 1.953741102 -0.444672175 0.756466966 0.243527026 1.416925126
#> [776] 2.760804810 2.541929371 0.546804523 1.987535104 1.796850202
#> [781] 1.730550767 1.263984715 1.718777933 2.913150783 0.430235311
#> [786] -2.594677130 1.512634342 2.516401034 1.664924810 1.818363144
#> [791] 2.434121005 1.296887450 -0.607499824 2.325647225 1.204393772
#> [796] 2.102347819 2.733846898 0.337568438 0.833849306 2.115166699
#> [801] 1.963385682 1.840510719 -1.101916765 1.493099351 2.053216162
#> [806] 1.492416312 1.825680812 2.038135102 2.877921593 2.423276235
#> [811] 2.785987623 2.623200234 -1.410558257 -2.483445403 2.701663000
#> [816] 1.962161460 2.185405353 1.507663210 1.048002417 1.956039388
#> [821] 2.181570265 0.828321712 0.668192270 1.660397117 2.394752488
#> [826] 0.088893485 0.245975815 -1.179627386 2.231532493 0.736509437
#> [831] 1.814178265 -4.103989740 0.392456053 1.842630093 1.103548536
#> [836] 1.719493997 1.409181440 2.283453572 1.016476009 0.338862939
#> [841] 2.397160158 2.341232594 2.842266126 2.732113005 -0.367626092
#> [846] 1.905455500 2.654534195 1.021420805 1.551194711 2.765761967
#> [851] -0.061838792 2.069658550 0.989402256 1.948440750 1.888545624
#> [856] 1.780201921 2.382474822 2.627472841 2.232907843 2.270721679
#> [861] 1.743436715 2.855044302 2.821632861 2.468345780 2.024210336
#> [866] 2.235075531 2.417341754 0.637830887 1.907621832 -0.451240503
#> [871] 2.559979024 -0.719477862 2.717998104 2.541055691 2.428884938
#> [876] 0.337657183 2.002175698 1.752197025 1.600542640 -1.533534306
#> [881] 0.279162499 2.741517612 -0.958433819 1.336112585 1.690040524
#> [886] 0.451787241 2.886987962 2.268741701 2.101829175 -0.582496847
#> [891] 1.672258788 2.268757824 0.147126591 0.723264128 2.331535459
#> [896] 2.289519671 0.031294849 -2.467061302 1.796464936 2.515780890
#> [901] 1.577385942 2.335547924 2.922991682 -0.271043076 2.671833408
#> [906] 1.815019279 0.590464578 1.290614854 1.095054594 1.185197451
#> [911] 0.484433344 2.107456446 0.842602627 2.266094666 -0.254906265
#> [916] 2.161855327 -1.115203308 2.299397685 2.146424463 2.816934261
#> [921] -0.964136698 0.598154178 2.294275322 1.578979458 2.770307910
#> [926] 1.258211367 3.001519185 2.775261048 2.113276708 -1.323198501
#> [931] 0.422879000 2.697013646 0.830819776 2.545402760 2.487647862
#> [936] 2.674038707 0.970101008 0.812646369 -1.216799106 2.252396583
#> [941] 2.353309742 2.164283015 0.416853659 -0.049733281 0.280131000
#> [946] 0.781359304 0.991440964 1.234283898 1.309497909 -0.568653719
#> [951] 2.526208628 1.923223643 -0.525080334 1.890238407 -0.707507184
#> [956] 2.410172304 2.029714024 2.498869488 2.970567330 -0.867130850
#> [961] 0.347151228 1.346623267 -1.045380606 0.570445454 1.114472748
#> [966] 1.879747853 2.375683628 -1.612098621 1.847696878 2.769574928
#> [971] 0.252917137 1.912650574 2.462870381 2.935004076 2.185000514
#> [976] 1.765057480 2.195086887 1.563311590 0.986990241 2.493392190
#> [981] -0.341869731 2.523040429 1.946603755 2.245762526 0.742687542
#> [986] 2.444120811 2.568770480 0.826523449 1.789031637 2.387431327
#> [991] 2.238121768 1.731182796 1.816183367 2.626779145 2.611494048
#> [996] 2.791274561 2.307493125 1.765595691 2.144054579 1.594237432