nag_rand_exp_mix (g05sgc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rand_exp_mix (g05sgc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_exp_mix (g05sgc) generates a vector of pseudorandom numbers from an exponential mix distribution composed of m exponential distributions each having a mean ai and weight wi.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_exp_mix (Integer n, Integer nmix, const double a[], const double wgt[], Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx = i=1m 1ai wi e-x/ai if ​x0, fx = 0 otherwise,
where i=1mwi=1 and ai>0, wi0.
nag_rand_exp_mix (g05sgc) returns the values xi by selecting, with probability wj, random variates from an exponential distribution with argument aj.
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_exp_mix (g05sgc).

4  References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

5  Arguments

1:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     nmixIntegerInput
On entry: m, the number of exponential distributions in the mix.
Constraint: nmix1.
3:     a[nmix]const doubleInput
On entry: the m parameters ai for the m exponential distributions in the mix.
Constraint: a[i-1]>0.0, for i=1,2,,nmix.
4:     wgt[nmix]const doubleInput
On entry: the m weights wi for the m exponential distributions in the mix.
  • i=1mwgt[i-1]=1.0;
  • wgt[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[n]doubleOutput
On exit: the n pseudorandom numbers from the specified exponential mix distribution.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

Dynamic memory allocation failed.
On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
On entry, nmix=value.
Constraint: nmix1.
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.
On entry, state vector has been corrupted or not initialized.
On entry, a[value]=value.
Constraint: a[i-1]>0.0.
On entry, sum of wgt=value.
Constraint: sum of wgt=1.0.
On entry, wgt[value]=value.
Constraint: wgt[i-1]0.0.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints the first five pseudorandom numbers from an exponential mix distribution comprising three exponential distributions with parameters a1=1.0, a2=5.0 and a3=2.0, and with respective weights 0.5, 0.3 and 0.2. The numbers are generated by a single call to nag_rand_exp_mix (g05sgc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05sgce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05sgce.r)

nag_rand_exp_mix (g05sgc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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