Description Usage Arguments Details Value References Examples
View source: R/rSingularWishart.R
Generate n
random matrices, distributed according to the Wishart distribution with parameters Sigma
and df
, W_p(Sigma, df).
1 | rSingularWishart(n, df, Sigma, covariance = FALSE, simplify = "array")
|
n |
integer: the number of replications. |
df |
numeric parameter, “degrees of freedom”. |
Sigma |
positive definite (p * p) “scale” matrix, the matrix parameter of the distribution. |
covariance |
logical on whether a covariance matrix should be generated |
simplify |
logical or character string; should the result be
simplified to a vector, matrix or higher dimensional array if
possible? For |
If X_1, ..., X_m is a sample of m independent multivariate Gaussians with mean vector 0, and covariance matrix Sigma, the distribution of M = X'X is W_p(Sigma, m).
A numeric array of dimension p * p * n
, where each array is a positive semidefinite matrix, a realization of the Wishart distribution W_p(Sigma, df)
Uhlig, Harald. 1994. “On Singular Wishart and Singular Multivariate Beta Distributions.” The Annals of Statistics 22 (1): 395–405. doi:10.1214/aos/1176325375.
1 | rSingularWishart(2, 5, diag(1, 20))
|
Attaching package: ‘rWishart’
The following object is masked from ‘package:stats’:
rWishart
, , 1
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 2.24594595 0.20416114 -2.8088324 -0.9392127 1.2409473 -1.1433585
[2,] 0.20416114 4.05954463 0.1588047 -2.7967496 -1.0342127 0.5061729
[3,] -2.80883237 0.15880473 5.7851403 2.4084655 -1.3497167 0.9973122
[4,] -0.93921269 -2.79674961 2.4084655 7.0021272 -1.5708844 0.1495864
[5,] 1.24094730 -1.03421268 -1.3497167 -1.5708844 2.2151027 -1.1809569
[6,] -1.14335846 0.50617291 0.9973122 0.1495864 -1.1809569 0.9462936
[7,] -0.41019042 -0.06813676 -3.1774679 -4.0462186 0.3587987 0.5909168
[8,] -0.93391505 1.32345535 1.5480094 -3.6743119 0.9103832 0.2483523
[9,] 2.25330671 0.24305529 -1.6368967 -1.8441303 2.7150242 -2.1798768
[10,] 1.32549976 0.95888106 -1.0945575 -2.3404514 1.6758697 -1.2272822
[11,] -1.21355092 -0.81506179 0.2843817 2.4783331 -2.2370270 1.5516170
[12,] -1.68866398 1.83660512 4.4683786 -1.4200441 0.2432557 0.1205373
[13,] -1.33041064 4.41154672 2.9238698 -1.9168502 -1.7922529 0.9972818
[14,] -1.97519224 0.65321707 1.2054573 -0.8866949 -1.2793482 1.2400148
[15,] -0.03393561 -2.65687129 -0.4400471 0.9298185 0.8944527 -0.1234071
[16,] 1.81590141 -0.80004867 -3.7933019 -2.0269403 1.6391525 -0.9345286
[17,] -0.14805382 1.41468406 -0.3025584 -4.4069656 1.3315105 -0.2618671
[18,] 0.01070160 -2.94778131 1.4557559 3.8857154 1.1582291 -1.4163182
[19,] -1.93650954 -0.52280108 3.6981571 6.2256232 -3.3645831 1.4917236
[20,] 0.06342989 -2.01372149 0.5799692 -0.7919519 2.1576278 -0.7696287
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] -0.410190420 -0.9339150 2.25330671 1.3254998 -1.213550915 -1.6886640
[2,] -0.068136755 1.3234553 0.24305529 0.9588811 -0.815061790 1.8366051
[3,] -3.177467880 1.5480094 -1.63689672 -1.0945575 0.284381697 4.4683786
[4,] -4.046218585 -3.6743119 -1.84413026 -2.3404514 2.478333053 -1.4200441
[5,] 0.358798701 0.9103832 2.71502416 1.6758697 -2.237027020 0.2432557
[6,] 0.590916763 0.2483523 -2.17987679 -1.2272822 1.551617027 0.1205373
[7,] 7.469808356 1.3353296 -0.36362844 0.5064454 -0.001367755 -1.5816357
[8,] 1.335329600 3.7660433 0.78459178 1.2242802 -1.966410217 3.6495855
[9,] -0.363628442 0.7845918 6.64476449 4.3269542 -5.553426163 2.0559183
[10,] 0.506445442 1.2242802 4.32695416 3.0856963 -3.883482188 1.8842331
[11,] -0.001367755 -1.9664102 -5.55342616 -3.8834822 5.186018440 -3.3476286
[12,] -1.581635714 3.6495855 2.05591834 1.8842331 -3.347628566 6.5146938
[13,] -0.726436225 2.2324497 0.08823838 0.9743422 -1.338950480 4.4972679
[14,] 3.036814125 1.2116054 -1.74122194 -0.6139236 0.729288284 1.1779296
[15,] 0.103124185 -0.3660353 -1.34347176 -1.3336700 1.489514469 -1.8424931
[16,] 2.623605015 -0.3983096 1.86780588 1.2180473 -0.991985646 -2.4439069
[17,] 3.215517677 3.2505357 2.69906695 2.5607319 -3.318243149 2.9941185
[18,] -1.893202505 -1.3260934 3.92055588 1.7351714 -2.951841411 1.5781417
[19,] -4.568734985 -2.9963924 -5.07246269 -3.9951570 4.738283363 -1.0233656
[20,] -0.300844865 1.7072918 1.40301576 0.7107684 -1.505443816 1.2521331
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] -1.33041064 -1.97519224 -0.03393561 1.8159014 -0.1480538 0.010701597
[2,] 4.41154672 0.65321707 -2.65687129 -0.8000487 1.4146841 -2.947781306
[3,] 2.92386975 1.20545729 -0.44004706 -3.7933019 -0.3025584 1.455755945
[4,] -1.91685025 -0.88669490 0.92981853 -2.0269403 -4.4069656 3.885715355
[5,] -1.79225287 -1.27934815 0.89445266 1.6391525 1.3315105 1.158229060
[6,] 0.99728178 1.24001477 -0.12340711 -0.9345286 -0.2618671 -1.416318151
[7,] -0.72643622 3.03681412 0.10312419 2.6236050 3.2155177 -1.893202505
[8,] 2.23244974 1.21160545 -0.36603533 -0.3983096 3.2505357 -1.326093441
[9,] 0.08823838 -1.74122194 -1.34347176 1.8678059 2.6990669 3.920555876
[10,] 0.97434221 -0.61392358 -1.33367003 1.2180473 2.5607319 1.735171359
[11,] -1.33895048 0.72928828 1.48951447 -0.9919856 -3.3182431 -2.951841411
[12,] 4.49726794 1.17792965 -1.84249313 -2.4439069 2.9941185 1.578141737
[13,] 6.46951864 1.89116573 -3.51881953 -2.5493892 2.0198679 -1.606507074
[14,] 1.89116573 2.97462728 -0.75937831 -0.7670735 1.5039478 -0.811714284
[15,] -3.51881953 -0.75937831 2.64170327 0.7328503 -1.1756367 -0.010596947
[16,] -2.54938923 -0.76707346 0.73285029 2.8959122 0.9503066 -0.174824326
[17,] 2.01986788 1.50394784 -1.17563669 0.9503066 4.2878915 -0.149801984
[18,] -1.60650707 -0.81171428 -0.01059695 -0.1748243 -0.1498020 7.342627096
[19,] 0.64319167 0.03415299 0.25510453 -3.6468120 -5.0194956 -0.003528435
[20,] -2.11187886 -0.90905266 1.91286320 0.6254062 1.0707149 1.317837060
[,19] [,20]
[1,] -1.936509540 0.06342989
[2,] -0.522801083 -2.01372149
[3,] 3.698157126 0.57996920
[4,] 6.225623154 -0.79195187
[5,] -3.364583144 2.15762781
[6,] 1.491723601 -0.76962869
[7,] -4.568734985 -0.30084486
[8,] -2.996392424 1.70729185
[9,] -5.072462692 1.40301576
[10,] -3.995156986 0.71076836
[11,] 4.738283363 -1.50544382
[12,] -1.023365591 1.25213305
[13,] 0.643191668 -2.11187886
[14,] 0.034152994 -0.90905266
[15,] 0.255104531 1.91286320
[16,] -3.646812038 0.62540624
[17,] -5.019495620 1.07071488
[18,] -0.003528435 1.31783706
[19,] 8.576101846 -2.26791529
[20,] -2.267915286 3.32513598
, , 2
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 9.6987359 3.9923727 -0.2315783 0.3026180 5.4801702 -3.0238208
[2,] 3.9923727 3.7931672 -0.1035219 -0.8575663 4.7836950 -2.0465555
[3,] -0.2315783 -0.1035219 12.0773996 -2.0507346 2.0552975 6.4100175
[4,] 0.3026180 -0.8575663 -2.0507346 1.3667227 -0.5179042 -1.5068604
[5,] 5.4801702 4.7836950 2.0552975 -0.5179042 8.6824122 -1.1159144
[6,] -3.0238208 -2.0465555 6.4100175 -1.5068604 -1.1159144 7.5917121
[7,] 0.4840630 1.9167546 5.3757119 -1.6502183 3.4818877 2.2301495
[8,] 2.7787013 1.1204779 -0.4423874 0.7331256 0.8576445 -3.9670532
[9,] -3.5560647 -4.7612687 -2.9655476 2.8878459 -3.1863790 2.2027578
[10,] 2.2729954 3.8535592 -1.1898375 -0.4860826 5.2797352 -3.2788718
[11,] -3.2786812 -2.4901536 2.3658634 0.6074890 -2.7307809 0.7107934
[12,] -1.5097028 -0.2336061 -0.3537399 0.8673868 1.5061714 -0.5059144
[13,] -1.3235072 -2.4396155 1.9671003 0.2898915 -2.3819874 3.2166254
[14,] -3.6093028 -1.5030339 -3.2337508 0.5862051 -3.8584915 -2.8385019
[15,] 4.2653104 3.0628211 -1.4144668 -0.1883655 1.7028850 -5.6845936
[16,] -0.5679943 -1.0777570 2.0891299 -0.0990132 -1.0022390 1.8830446
[17,] 5.2962160 1.4359408 3.1313568 0.2245969 4.6205615 2.2403539
[18,] 0.1133549 -0.2749000 0.6935404 0.8440361 1.2937554 -0.1668140
[19,] 8.0788229 4.7941537 -0.5163439 -0.7399572 5.1355214 -3.5660199
[20,] 3.0010035 1.9070081 -6.1641122 -0.1616952 -1.6011026 -5.4085333
[,7] [,8] [,9] [,10] [,11] [,12]
[1,] 0.4840630 2.77870129 -3.5560647 2.27299543 -3.2786812 -1.50970283
[2,] 1.9167546 1.12047788 -4.7612687 3.85355925 -2.4901536 -0.23360613
[3,] 5.3757119 -0.44238742 -2.9655476 -1.18983746 2.3658634 -0.35373987
[4,] -1.6502183 0.73312557 2.8878459 -0.48608263 0.6074890 0.86738675
[5,] 3.4818877 0.85764450 -3.1863790 5.27973522 -2.7307809 1.50617144
[6,] 2.2301495 -3.96705315 2.2027578 -3.27887184 0.7107934 -0.50591436
[7,] 3.8339585 -0.25306845 -3.8272783 1.96057560 -0.1521613 0.19528856
[8,] -0.2530684 3.63909579 -2.6550726 1.41202181 0.8307033 -0.05492467
[9,] -3.8272783 -2.65507262 12.2099112 -4.20696588 1.8463248 2.66368642
[10,] 1.9605756 1.41202181 -4.2069659 5.21989851 -1.8396064 1.23006556
[11,] -0.1521613 0.83070334 1.8463248 -1.83960636 3.4222888 0.91043230
[12,] 0.1952886 -0.05492467 2.6636864 1.23006556 0.9104323 2.39489165
[13,] -0.6407410 -1.47539216 3.5801314 -3.33852810 1.1375667 -0.32298848
[14,] -1.8955274 1.31832970 -0.1855433 -0.27503320 1.9028843 0.26271207
[15,] 0.3359441 4.49355513 -7.0578025 3.18024718 -0.5650648 -1.24590838
[16,] 0.2337000 -0.49849513 0.9766758 -1.60365506 0.8233940 -0.29249083
[17,] 1.3860708 -0.60128848 1.6683949 0.04601831 -1.7731288 0.12403236
[18,] 0.1524857 0.42893303 2.1872606 0.34197429 0.8685511 1.50858409
[19,] 1.3239744 2.74955606 -6.7938989 3.58426393 -3.5003534 -1.91486278
[20,] -2.3408978 2.35619738 -5.1248581 1.32480301 -2.2512005 -2.63821070
[,13] [,14] [,15] [,16] [,17] [,18]
[1,] -1.3235072 -3.6093028 4.2653104 -0.5679943 5.29621596 0.1133549
[2,] -2.4396155 -1.5030339 3.0628211 -1.0777570 1.43594083 -0.2749000
[3,] 1.9671003 -3.2337508 -1.4144668 2.0891299 3.13135677 0.6935404
[4,] 0.2898915 0.5862051 -0.1883655 -0.0990132 0.22459694 0.8440361
[5,] -2.3819874 -3.8584915 1.7028850 -1.0022390 4.62056150 1.2937554
[6,] 3.2166254 -2.8385019 -5.6845936 1.8830446 2.24035386 -0.1668140
[7,] -0.6407410 -1.8955274 0.3359441 0.2337000 1.38607077 0.1524857
[8,] -1.4753922 1.3183297 4.4935551 -0.4984951 -0.60128848 0.4289330
[9,] 3.5801314 -0.1855433 -7.0578025 0.9766758 1.66839495 2.1872606
[10,] -3.3385281 -0.2750332 3.1802472 -1.6036551 0.04601831 0.3419743
[11,] 1.1375667 1.9028843 -0.5650648 0.8233940 -1.77312877 0.8685511
[12,] -0.3229885 0.2627121 -1.2459084 -0.2924908 0.12403236 1.5085841
[13,] 2.5532199 -0.8663158 -3.1623321 1.2562465 1.21830519 0.2340636
[14,] -0.8663158 4.2816901 1.7799790 -0.5314361 -4.96724967 -0.4342409
[15,] -3.1623321 1.7799790 7.3436379 -1.2294407 -1.71582483 -0.7277697
[16,] 1.2562465 -0.5314361 -1.2294407 0.7558475 0.65162565 0.1019345
[17,] 1.2183052 -4.9672497 -1.7158248 0.6516257 6.51518630 1.1748126
[18,] 0.2340636 -0.4342409 -0.7277697 0.1019345 1.17481264 1.3379079
[19,] -2.6185452 -2.2407430 5.6120630 -1.0867325 2.79360537 -0.8364576
[20,] -2.4816194 2.5092530 5.5764570 -1.4506686 -3.07891186 -2.2584859
[,19] [,20]
[1,] 8.0788229 3.0010035
[2,] 4.7941537 1.9070081
[3,] -0.5163439 -6.1641122
[4,] -0.7399572 -0.1616952
[5,] 5.1355214 -1.6011026
[6,] -3.5660199 -5.4085333
[7,] 1.3239744 -2.3408978
[8,] 2.7495561 2.3561974
[9,] -6.7938989 -5.1248581
[10,] 3.5842639 1.3248030
[11,] -3.5003534 -2.2512005
[12,] -1.9148628 -2.6382107
[13,] -2.6185452 -2.4816194
[14,] -2.2407430 2.5092530
[15,] 5.6120630 5.5764570
[16,] -1.0867325 -1.4506686
[17,] 2.7936054 -3.0789119
[18,] -0.8364576 -2.2584859
[19,] 8.2929082 4.6214287
[20,] 4.6214287 8.3067717
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