One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_dist_dirichlet (g05se).

References

Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press

Hastings N A J and Peacock J B (1975) Statistical Distributions Butterworth

Parameters

Compulsory Input Parameters

1: $n$ – int64int32nag_int scalar: $n$ , the number of pseudorandom numbers to be generated.

Constraint: $n \geq 0$ .
2: $a (m)$ – double array: The parameter vector for the distribution.

Constraint: $a (i) > 0.0$ , for $i = 1, 2, \dots, m$ .
3: $state (:)$ – int64int32nag_int array: Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

1: $m$ – int64int32nag_int scalar: Default: the dimension of the array a.
$m$ , the number of dimensions of the distribution.

Constraint: $m > 0$ .

Output Parameters

1: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
2: $x (ldx, m)$ – double array: The $n$ pseudorandom numbers from the specified Dirichlet distribution, with $x (i, j)$ holding the $j$ th dimension for the $i$ th variate.
3: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $n \geq 0$ .

$ifail = 2$: Constraint: $m > 0$ .

$ifail = 3$: On entry, at least one $a (i) \leq 0$ .

$ifail = 4$: On entry, state vector has been corrupted or not initialized.

$ifail = 6$: Constraint: $ldx \geq n$ .

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

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_dist_dirichlet (g05se), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05se_example

function g05se_example


fprintf('g05se example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Number of variates
n = int64(5);
% Parameters
a = [2; 2; 2; 2];

% Generate variates from Dirichlet distribution
[state, x, ifail] = g05se( ...
                           n, a, state);

disp('Variates');
disp(x);

g05se example results

Variates
    0.3600    0.3138    0.0837    0.2426
    0.2874    0.5121    0.1497    0.0509
    0.2286    0.2190    0.3959    0.1566
    0.1744    0.3961    0.2764    0.1530
    0.1522    0.2845    0.2074    0.3559

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox