A function to sample Dirichlet random variables, based on the representation as ratios of Gamma. Note that the RNG will generate on the full simplex and the sum to one constraint is respected here
Examples
rdir(n=100, alpha=c(0.5,0.5,2),TRUE)
#> [,1] [,2] [,3]
#> [1,] 7.369649e-02 0.0765378033 0.8497657
#> [2,] 2.311068e-01 0.4353898871 0.3335033
#> [3,] 1.552036e-01 0.0783630225 0.7664334
#> [4,] 2.182047e-01 0.0426221842 0.7391732
#> [5,] 7.140462e-01 0.1021241124 0.1838297
#> [6,] 4.954060e-02 0.0022511560 0.9482082
#> [7,] 3.418142e-02 0.2011327504 0.7646858
#> [8,] 1.313665e-02 0.0843731177 0.9024902
#> [9,] 3.055985e-01 0.0349449043 0.6594566
#> [10,] 2.318918e-01 0.0925978215 0.6755104
#> [11,] 7.504584e-03 0.0771184493 0.9153770
#> [12,] 7.147811e-03 0.0251158934 0.9677363
#> [13,] 6.339870e-01 0.0030634436 0.3629496
#> [14,] 8.855816e-02 0.2048948574 0.7065470
#> [15,] 6.796217e-03 0.0010661235 0.9921377
#> [16,] 1.984315e-03 0.2801299603 0.7178857
#> [17,] 2.278089e-03 0.1308096919 0.8669122
#> [18,] 2.506997e-02 0.1946339132 0.7802961
#> [19,] 2.383513e-02 0.1333190629 0.8428458
#> [20,] 1.111688e-01 0.0733469955 0.8154842
#> [21,] 6.198885e-01 0.0720251022 0.3080864
#> [22,] 4.910645e-01 0.0690836947 0.4398518
#> [23,] 1.698968e-01 0.2915551808 0.5385480
#> [24,] 3.177091e-01 0.0315200359 0.6507709
#> [25,] 1.069836e-01 0.1473328591 0.7456835
#> [26,] 3.064791e-02 0.0204866398 0.9488654
#> [27,] 9.131042e-02 0.0844671051 0.8242225
#> [28,] 9.901256e-03 0.7091638378 0.2809349
#> [29,] 1.101397e-01 0.1973826652 0.6924776
#> [30,] 1.856709e-01 0.0329121903 0.7814169
#> [31,] 6.687670e-02 0.0998275613 0.8332957
#> [32,] 3.440934e-02 0.0338974309 0.9316932
#> [33,] 7.663968e-05 0.2268024272 0.7731209
#> [34,] 7.127407e-02 0.4046925226 0.5240334
#> [35,] 5.389910e-02 0.0519251114 0.8941758
#> [36,] 2.590589e-02 0.0568036681 0.9172904
#> [37,] 9.498001e-02 0.0181748562 0.8868451
#> [38,] 7.617966e-01 0.0041816480 0.2340217
#> [39,] 1.076328e-01 0.5866685442 0.3056987
#> [40,] 8.562890e-02 0.1395148617 0.7748562
#> [41,] 1.907166e-01 0.0568336421 0.7524498
#> [42,] 2.616550e-01 0.0124969250 0.7258481
#> [43,] 4.313003e-01 0.0253662961 0.5433334
#> [44,] 9.399444e-03 0.1568176826 0.8337829
#> [45,] 3.677795e-01 0.2164950949 0.4157254
#> [46,] 2.475853e-01 0.0041190776 0.7482957
#> [47,] 9.289539e-02 0.0750808246 0.8320238
#> [48,] 2.572678e-01 0.0181135487 0.7246186
#> [49,] 3.862775e-01 0.0862304637 0.5274921
#> [50,] 3.478451e-04 0.2530317691 0.7466204
#> [51,] 2.841905e-02 0.1649836882 0.8065973
#> [52,] 6.876566e-03 0.0528202418 0.9403032
#> [53,] 1.472265e-01 0.1134206562 0.7393529
#> [54,] 6.609456e-02 0.4709766905 0.4629288
#> [55,] 5.336126e-01 0.0144474098 0.4519400
#> [56,] 1.666306e-01 0.0381576436 0.7952117
#> [57,] 8.154915e-02 0.7013425741 0.2171083
#> [58,] 9.355152e-02 0.0033538285 0.9030947
#> [59,] 8.135511e-03 0.4556697392 0.5361947
#> [60,] 2.606364e-01 0.0055309842 0.7338327
#> [61,] 8.950617e-02 0.0891867471 0.8213071
#> [62,] 2.695722e-03 0.8073763926 0.1899279
#> [63,] 1.643465e-02 0.3419713225 0.6415940
#> [64,] 4.221305e-02 0.1137491508 0.8440378
#> [65,] 1.156145e-04 0.7251124422 0.2747719
#> [66,] 1.991125e-02 0.1082286717 0.8718601
#> [67,] 2.297183e-01 0.2105580712 0.5597236
#> [68,] 2.014650e-03 0.0899986970 0.9079867
#> [69,] 4.896003e-02 0.0194882319 0.9315517
#> [70,] 2.591126e-04 0.3471344026 0.6526065
#> [71,] 5.704946e-03 0.4023671740 0.5919279
#> [72,] 2.592707e-01 0.1259765895 0.6147527
#> [73,] 6.163806e-02 0.0259790864 0.9123829
#> [74,] 1.325899e-01 0.0015947716 0.8658154
#> [75,] 1.939124e-01 0.2708384203 0.5352491
#> [76,] 1.173954e-02 0.0063440203 0.9819164
#> [77,] 1.056518e-02 0.4140896119 0.5753452
#> [78,] 2.920152e-01 0.0113226302 0.6966622
#> [79,] 2.673810e-01 0.0185421528 0.7140769
#> [80,] 9.046118e-02 0.0002462465 0.9092926
#> [81,] 5.296684e-02 0.1210221461 0.8260110
#> [82,] 9.411097e-06 0.5387013687 0.4612892
#> [83,] 3.022372e-04 0.3152238190 0.6844739
#> [84,] 4.895891e-04 0.0003463612 0.9991640
#> [85,] 9.633849e-03 0.3949001041 0.5954660
#> [86,] 1.360569e-01 0.0014228178 0.8625202
#> [87,] 1.411284e-02 0.1243983192 0.8614888
#> [88,] 2.822394e-02 0.0308136310 0.9409624
#> [89,] 1.537854e-01 0.0610251617 0.7851895
#> [90,] 1.363112e-01 0.1926706587 0.6710182
#> [91,] 6.910669e-01 0.0131130571 0.2958201
#> [92,] 1.200728e-01 0.0201652134 0.8597620
#> [93,] 2.094298e-01 0.5009609511 0.2896093
#> [94,] 4.403166e-02 0.0683066188 0.8876617
#> [95,] 8.838625e-02 0.0735689354 0.8380448
#> [96,] 4.751124e-01 0.1803503826 0.3445372
#> [97,] 3.903883e-01 0.0027770676 0.6068346
#> [98,] 2.490775e-01 0.0519544858 0.6989680
#> [99,] 9.759119e-02 0.1425127388 0.7598961
#> [100,] 1.011836e-01 0.0941766302 0.8046398
rdir(n=100, alpha=c(3,1,2),FALSE)
#> [,1] [,2] [,3]
#> [1,] 0.5191856 0.5657185102 1.3476165
#> [2,] 3.0572454 0.7587096401 0.4957867
#> [3,] 0.6712289 2.8103192174 1.3739499
#> [4,] 1.7766274 0.5149119876 5.7753507
#> [5,] 5.1980112 0.7468086972 0.8712667
#> [6,] 0.7832317 0.3207621807 1.8251169
#> [7,] 1.8164491 1.5091178701 1.4199056
#> [8,] 3.8437073 0.6332100661 0.1707316
#> [9,] 3.0454307 3.1648358410 3.1156613
#> [10,] 5.8064077 0.1407429512 3.6765402
#> [11,] 1.8641454 0.8455789518 7.4137553
#> [12,] 1.1736300 1.0091973208 0.7443287
#> [13,] 2.9713201 1.6507309538 1.7703679
#> [14,] 4.1716465 1.0172656245 1.8056013
#> [15,] 2.9324668 0.1310734689 1.4503016
#> [16,] 5.2781363 1.8206847439 3.9430276
#> [17,] 2.2138287 0.4456008300 4.5642070
#> [18,] 3.4872290 1.0653057445 1.3334971
#> [19,] 0.5402611 1.3250083198 0.7437200
#> [20,] 4.9117105 0.7281726592 2.2953126
#> [21,] 5.2280549 1.9847455145 4.3790928
#> [22,] 5.2264994 0.5332433678 0.7037596
#> [23,] 1.3405926 0.4362851616 5.1107455
#> [24,] 3.4540471 1.3620054950 1.3822771
#> [25,] 1.5716870 3.1221060284 3.6317457
#> [26,] 2.6902309 0.3619814708 4.3218787
#> [27,] 6.0405311 1.1078187527 1.7560398
#> [28,] 5.9088640 0.7410845114 0.3513223
#> [29,] 1.7903857 0.4182348277 0.1108663
#> [30,] 4.0502163 1.1828106707 1.4690982
#> [31,] 3.9763782 1.7447769643 4.7056762
#> [32,] 1.5329652 4.0111959302 1.0538613
#> [33,] 1.9134197 1.6225686887 1.4834122
#> [34,] 3.8662030 0.2951403905 4.5781610
#> [35,] 1.4242328 3.0645625208 0.6588286
#> [36,] 2.3109077 0.5853459076 0.8717445
#> [37,] 3.8799819 0.1762865452 0.4648718
#> [38,] 1.0383487 0.6933322538 0.6367161
#> [39,] 1.7879741 1.0049423177 4.4566953
#> [40,] 4.0967402 0.6254848029 5.0710935
#> [41,] 4.3214311 0.6297074165 1.6134154
#> [42,] 2.0034124 1.2979098231 3.2159645
#> [43,] 1.6896058 0.7033967821 1.5912472
#> [44,] 1.1215118 1.0039404008 1.2300292
#> [45,] 2.5165104 0.5122206085 1.3831104
#> [46,] 3.8222020 0.2321090862 1.2181405
#> [47,] 6.8946794 1.4351358269 1.4746009
#> [48,] 1.0387056 0.5334038538 4.0083240
#> [49,] 4.5091487 0.1375620674 2.0511536
#> [50,] 1.3306141 0.5830652704 3.5368835
#> [51,] 1.7000354 0.1623763747 0.9035040
#> [52,] 4.5675359 1.6294349226 0.5030574
#> [53,] 3.7579045 4.3537183223 0.5061478
#> [54,] 4.5876322 0.5801321390 0.3782676
#> [55,] 7.0260941 0.1275199147 1.7001996
#> [56,] 4.4090710 0.4754320172 6.3471173
#> [57,] 2.1176563 1.7518338924 0.9398455
#> [58,] 1.5590015 0.4105680200 4.1161434
#> [59,] 1.9336569 1.3302181298 5.0938611
#> [60,] 0.9604132 0.3157753431 1.0847309
#> [61,] 3.2304251 1.8045651408 2.4803022
#> [62,] 1.1478336 1.5282867316 1.4989679
#> [63,] 3.8511378 1.1209671502 1.3281819
#> [64,] 3.1761339 3.1254713993 1.8640920
#> [65,] 3.5362214 1.1038261523 2.0277034
#> [66,] 0.8296751 0.0716374256 1.2411745
#> [67,] 1.6655442 7.8322391665 0.7619994
#> [68,] 4.4486161 2.6607105374 2.4260625
#> [69,] 2.7995609 3.8071390025 1.2952952
#> [70,] 6.9166534 0.0219043313 1.6299354
#> [71,] 2.9564156 3.0130172097 3.4486462
#> [72,] 2.3180321 0.4031472426 6.5958056
#> [73,] 3.0984318 0.4431342734 1.4009734
#> [74,] 4.1619789 1.0643301617 3.3788266
#> [75,] 2.2406345 2.3717957308 0.5126196
#> [76,] 2.8405126 1.3682749829 1.0031464
#> [77,] 3.0856193 0.8970408785 3.0025300
#> [78,] 3.2910129 0.8657499801 0.5113335
#> [79,] 4.0228616 1.4653744747 1.9375124
#> [80,] 0.4335552 2.0972002653 1.9818001
#> [81,] 0.4600798 0.9791579351 1.3472679
#> [82,] 1.7154897 1.4873921369 1.1390135
#> [83,] 1.4581621 0.4943336982 1.6054939
#> [84,] 7.2077960 0.6215677808 1.7869377
#> [85,] 2.3611707 2.5012458704 0.4119828
#> [86,] 1.4592564 1.5373245435 0.3379988
#> [87,] 0.9967300 0.3453843085 1.5476422
#> [88,] 0.7037616 3.2810737506 1.0323901
#> [89,] 7.5508363 1.2662776511 1.9617336
#> [90,] 4.4722093 0.3799931302 4.5241559
#> [91,] 1.5447284 0.0721678259 1.3333920
#> [92,] 0.8987009 0.8667604376 1.5147813
#> [93,] 1.5747097 0.2764275411 1.4067947
#> [94,] 1.8487052 0.3943475888 1.3526483
#> [95,] 2.3353823 3.3625770511 0.8735704
#> [96,] 4.9237932 0.7460144623 1.0115178
#> [97,] 6.2148871 1.9870104106 0.5484934
#> [98,] 1.6386062 0.9349983750 0.5562714
#> [99,] 1.6367624 0.4635335813 1.6701824
#> [100,] 2.4702622 0.0006304142 1.4764322