nag_rand_gamma (g05sjc) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_gamma (g05sjc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_gamma (g05sjc) generates a vector of pseudorandom numbers taken from a gamma distribution with parameters a and b.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_gamma (Integer n, double a, double b, Integer state[], double x[], NagError *fail)

3  Description

The gamma distribution has PDF (probability density function)
fx= 1baΓa xa-1e-x/b if ​x0;  a,b>0 fx=0 otherwise.
One of three algorithms is used to generate the variates depending upon the value of a:
(i) if a<1, a switching algorithm described by Dagpunar (1988) (called G6) is used. The target distributions are f1x=caxa-1/ta and f2x=1-ce-x-t, where c=t/t+ae-t, and the switching argument, t, is taken as 1-a. This is similar to Ahrens and Dieter's GS algorithm (see Ahrens and Dieter (1974)) in which t=1;
(ii) if a=1, the gamma distribution reduces to the exponential distribution and the method based on the logarithmic transformation of a uniform random variate is used;
(iii) if a>1, the algorithm given by Best (1978) is used. This is based on using a Student's t-distribution with two degrees of freedom as the target distribution in an envelope rejection method.
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_gamma (g05sjc).

4  References

Ahrens J H and Dieter U (1974) Computer methods for sampling from gamma, beta, Poisson and binomial distributions Computing 12 223–46
Best D J (1978) Letter to the Editor Appl. Statist. 27 181
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:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     adoubleInput
On entry: a, the parameter of the gamma distribution.
Constraint: a>0.0.
3:     bdoubleInput
On entry: b, the parameter of the gamma distribution.
Constraint: b>0.0.
4:     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.
5:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified gamma distribution.
6:     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, n=value.
Constraint: n0.
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
On entry, a=value.
Constraint: a>0.0.
On entry, b=value.
Constraint: b>0.0.

7  Accuracy

Not applicable.

8  Further Comments

None.

9  Example

This example prints a set of five pseudorandom numbers from a gamma distribution with parameters a=5.0 and b=1.0, generated by a single call to nag_rand_gamma (g05sjc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05sjce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05sjce.r)


nag_rand_gamma (g05sjc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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