nag_rand_dirichlet (g05sec) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_dirichlet (g05sec)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_dirichlet (g05sec) generates a vector of pseudorandom numbers taken from a Dirichlet distribution.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_dirichlet (Nag_OrderType order, Integer n, Integer m, const double a[], Integer state[], double x[], Integer pdx, NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx = 1 Bα i=1 m x i αi - 1 and Bα = i=1 m Γ αi Γ i=1 m αi
where x = x1,x2,,xm  is a vector of dimension m, such that xi>0 for all i and i=1 m xi=1.
nag_rand_dirichlet (g05sec) generates a draw from a Dirichlet distribution by first drawing m independent samples, yigammaαi,1, i.e., independent draws from a gamma distribution with parameters αi>0 and one, and then setting xi=yi/ j=1 m yj.
One of the initialization functions nag_rand_init_repeatable (g05kfc) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeatable (g05kgc) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dirichlet (g05sec).

4  References

Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

5  Arguments

1:     orderNag_OrderTypeInput
On entry: the order argument specifies the two-dimensional storage scheme being used, i.e., row-major ordering or column-major ordering. C language defined storage is specified by order=Nag_RowMajor. See Section 3.2.1.3 in the Essential Introduction for a more detailed explanation of the use of this argument.
Constraint: order=Nag_RowMajor or Nag_ColMajor.
2:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     mIntegerInput
On entry: m, the number of dimensions of the distribution.
Constraint: m>0.
4:     a[m]const doubleInput
On entry: the parameter vector for the distribution.
Constraint: a[i-1]>0.0, for i=1,2,,m.
5:     state[dim]IntegerCommunication Array
Note: the actual argument supplied must be the array state supplied to the initialization functions nag_rand_init_repeatable (g05kfc) or nag_rand_init_nonrepeatable (g05kgc).
On entry: contains information on the selected base generator and its current state.
On exit: contains updated information on the state of the generator.
6:     x[dim]doubleOutput
Note: the dimension, dim, of the array x must be at least
  • max1,pdx×m when order=Nag_ColMajor;
  • max1,n×pdx when order=Nag_RowMajor.
Where Xi,j appears in this document, it refers to the array element
  • x[j-1×pdx+i-1] when order=Nag_ColMajor;
  • x[i-1×pdx+j-1] when order=Nag_RowMajor.
On exit: the n pseudorandom numbers from the specified Dirichlet distribution, with Xi,j holding the jth dimension for the ith variate.
7:     pdxIntegerInput
On entry: the stride separating row or column elements (depending on the value of order) in the array x.
Constraints:
  • if order=Nag_ColMajor, pdxn;
  • if order=Nag_RowMajor, pdxm.
8:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, m=value.
Constraint: m>0.
On entry, n=value.
Constraint: n0.
NE_INT_2
On entry, pdx=value and m=value.
Constraint: pdxm.
On entry, pdx=value and n=value.
Constraint: orderNag_ColMajor or pdxn.
NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_REAL_ARRAY
On entry, at least one a[i]0.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example prints a set of five pseudorandom numbers from a Dirichlet distribution with parameters m=4 and α=2.0,2.0,2.0,2.0, generated by a single call to nag_rand_dirichlet (g05sec), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05sece.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05sece.r)


nag_rand_dirichlet (g05sec) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012