nag_rngs_exp_mix (g05lqc) (PDF version)
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NAG C Library Manual

NAG Library Function Document

nag_rngs_exp_mix (g05lqc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_exp_mix (g05lqc) 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_rngs_exp_mix (Integer nmix, const double a[], const double wgt[], Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx= i=1m1aiwie-x/ai if ​x>0, 0 otherwise,
where i=1mwi=1 and ai>0, wi0.
nag_rngs_exp_mix (g05lqc) returns the values xi by selecting, with probability wj, random variates from an exponential distribution with parameter aj.
One of the initialization functions nag_rngs_init_repeatable (g05kbc) (for a repeatable sequence if computed sequentially) or nag_rngs_init_nonrepeatable (g05kcc) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_exp_mix (g05lqc).

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:     nmixIntegerInput
On entry: m, the number of exponential distributions in the mix.
Constraint: nmix1.
2:     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.
3:     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.
4:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
5:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified exponential mix distribution.
6:     igenIntegerInput
On entry: must contain the identification number for the generator to be used to return a pseudorandom number and should remain unchanged following initialization by a prior call to nag_rngs_init_repeatable (g05kbc) or nag_rngs_init_nonrepeatable (g05kcc).
7:     iseed[4]IntegerCommunication Array
On entry: contains values which define the current state of the selected generator.
On exit: contains updated values defining the new state of the selected generator.
8:     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, sum of weights wgt is not equal to 1.0: sum =value.
On entry, i=value and a[i-1]=value.
Constraint: a[i-1]>0.0.
On entry, i=value and wgt[i-1]=value.
Constraint: wgt[i-1]0.0.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints the first five pseudorandom real 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_rngs_exp_mix (g05lqc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lqce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05lqce.r)

nag_rngs_exp_mix (g05lqc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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