Dirichlet: The Dirichlet Distribution

Description Usage Arguments Details Value Author(s) Examples

Description

Density function and random number generation for the Dirichlet distribution

Usage

1
rdirichlet(n, alpha)

Arguments

n

number of random observations to draw

alpha

the Dirichlet distribution's parameters. Can be a vector (one set of parameters for all observations) or a matrix (a different set of parameters for each observation), see “Details”

Details

The Dirichlet distribution is a multidimensional generalization of the Beta distribution where each dimension is governed by an alpha-parameter. Formally this is

D(α)=[Γ(∑α)/∏Γ(α)]∏ y^(α-1)

Usually, alpha is a vector thus the same parameters will be used for all observations. If alpha is a matrix, a complete set of alpha-parameters must be supplied for each observation.

Value

returns a matrix with random numbers according to the supplied alpha vector or matrix.

Author(s)

Chong Wu

Examples

1
2
X1 <- rdirichlet(100, c(5, 5, 10))
X1

Example output

Loading required package: vegan
Loading required package: permute
Loading required package: lattice
This is vegan 2.5-4
Loading required package: ape
Loading required package: aSPU
Loading required package: gee
Loading required package: MASS
Loading required package: mvtnorm
Loading required package: fields
Loading required package: spam
Loading required package: dotCall64
Loading required package: grid
Spam version 2.2-2 (2019-03-07) is loaded.
Type 'help( Spam)' or 'demo( spam)' for a short introduction 
and overview of this package.
Help for individual functions is also obtained by adding the
suffix '.spam' to the function name, e.g. 'help( chol.spam)'.

Attaching package: 'spam'

The following objects are masked from 'package:base':

    backsolve, forwardsolve

Loading required package: maps
See https://github.com/NCAR/Fields for
 an extensive vignette, other supplements and source code 
Loading required package: matrixStats
Loading required package: cluster

Attaching package: 'cluster'

The following object is masked from 'package:maps':

    votes.repub

             [,1]       [,2]      [,3]
  [1,] 0.29105184 0.24806740 0.4608808
  [2,] 0.25382229 0.33254543 0.4136323
  [3,] 0.11365039 0.57758880 0.3087608
  [4,] 0.25860573 0.40678402 0.3346103
  [5,] 0.12746048 0.26510768 0.6074318
  [6,] 0.26751905 0.27356930 0.4589117
  [7,] 0.31176683 0.30055708 0.3876761
  [8,] 0.21664021 0.16004899 0.6233108
  [9,] 0.31093869 0.30607414 0.3829872
 [10,] 0.35615739 0.32370583 0.3201368
 [11,] 0.11284317 0.39429438 0.4928624
 [12,] 0.13753828 0.25636807 0.6060937
 [13,] 0.33833881 0.22959871 0.4320625
 [14,] 0.30661004 0.44370568 0.2496843
 [15,] 0.43039055 0.11684270 0.4527667
 [16,] 0.25165503 0.29395678 0.4543882
 [17,] 0.19939113 0.12156608 0.6790428
 [18,] 0.39172161 0.35856373 0.2497147
 [19,] 0.26490581 0.27751978 0.4575744
 [20,] 0.43525198 0.19792406 0.3668240
 [21,] 0.29484520 0.41945323 0.2857016
 [22,] 0.41528304 0.06847855 0.5162384
 [23,] 0.35908524 0.32313296 0.3177818
 [24,] 0.20850325 0.32757231 0.4639244
 [25,] 0.36970308 0.22289124 0.4074057
 [26,] 0.22034737 0.31856185 0.4610908
 [27,] 0.30277456 0.14689051 0.5503349
 [28,] 0.18405935 0.33721352 0.4787271
 [29,] 0.42371140 0.26275292 0.3135357
 [30,] 0.21123281 0.19619178 0.5925754
 [31,] 0.08900358 0.35445936 0.5565371
 [32,] 0.21268466 0.23258089 0.5547345
 [33,] 0.25741906 0.13555578 0.6070252
 [34,] 0.21032519 0.13018204 0.6594928
 [35,] 0.21662694 0.16256778 0.6208053
 [36,] 0.24368849 0.19508822 0.5612233
 [37,] 0.16601711 0.19571871 0.6382642
 [38,] 0.22441511 0.19064478 0.5849401
 [39,] 0.28591009 0.34904109 0.3650488
 [40,] 0.32171421 0.21767947 0.4606063
 [41,] 0.18372713 0.14384564 0.6724272
 [42,] 0.27299559 0.26801278 0.4589916
 [43,] 0.19577170 0.33440854 0.4698198
 [44,] 0.28540894 0.28218834 0.4324027
 [45,] 0.26129145 0.15253126 0.5861773
 [46,] 0.33044326 0.22850552 0.4410512
 [47,] 0.17690680 0.44385360 0.3792396
 [48,] 0.21753701 0.30270723 0.4797558
 [49,] 0.21473043 0.33983482 0.4454348
 [50,] 0.19907245 0.43788822 0.3630393
 [51,] 0.26771481 0.23118532 0.5010999
 [52,] 0.20343841 0.21889661 0.5776650
 [53,] 0.28493347 0.17253773 0.5425288
 [54,] 0.19705209 0.37115920 0.4317887
 [55,] 0.10464306 0.15683067 0.7385263
 [56,] 0.06269919 0.32598628 0.6113145
 [57,] 0.22658491 0.21825749 0.5551576
 [58,] 0.36851602 0.18977634 0.4417076
 [59,] 0.18208115 0.54158791 0.2763309
 [60,] 0.06605319 0.29271592 0.6412309
 [61,] 0.18292370 0.33488411 0.4821922
 [62,] 0.35449474 0.08682098 0.5586843
 [63,] 0.13539434 0.35287885 0.5117268
 [64,] 0.35699517 0.31191344 0.3310914
 [65,] 0.28440635 0.28779718 0.4277965
 [66,] 0.16983919 0.51101230 0.3191485
 [67,] 0.28582309 0.16311738 0.5510595
 [68,] 0.35316709 0.20914643 0.4376865
 [69,] 0.18100694 0.35365026 0.4653428
 [70,] 0.15003428 0.17484900 0.6751167
 [71,] 0.17752877 0.13926950 0.6832017
 [72,] 0.22539027 0.24638748 0.5282222
 [73,] 0.49304300 0.16871032 0.3382467
 [74,] 0.23255657 0.22139577 0.5460477
 [75,] 0.22035030 0.34052962 0.4391201
 [76,] 0.17699354 0.17766021 0.6453463
 [77,] 0.23604706 0.38301602 0.3809369
 [78,] 0.21343176 0.23439251 0.5521757
 [79,] 0.31161928 0.08573942 0.6026413
 [80,] 0.41622634 0.21524186 0.3685318
 [81,] 0.19359846 0.21342492 0.5929766
 [82,] 0.24115032 0.19473928 0.5641104
 [83,] 0.14985072 0.41543186 0.4347174
 [84,] 0.20582387 0.46132395 0.3328522
 [85,] 0.19151952 0.21742383 0.5910567
 [86,] 0.23016880 0.20197343 0.5678578
 [87,] 0.11852500 0.17587381 0.7056012
 [88,] 0.21284618 0.25637078 0.5307830
 [89,] 0.11756747 0.39038157 0.4920510
 [90,] 0.16492242 0.13921792 0.6958597
 [91,] 0.20511682 0.32775159 0.4671316
 [92,] 0.12333633 0.32684158 0.5498221
 [93,] 0.26340607 0.04689733 0.6896966
 [94,] 0.34402229 0.18886469 0.4671130
 [95,] 0.29172818 0.13348662 0.5747852
 [96,] 0.29539679 0.25075352 0.4538497
 [97,] 0.28938509 0.14724859 0.5633663
 [98,] 0.14071609 0.27769015 0.5815938
 [99,] 0.11608768 0.63164364 0.2522687
[100,] 0.10134970 0.29181076 0.6068395

MiSPU documentation built on May 1, 2019, 8:41 p.m.