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.
Constraints:
  • 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

NE_ALLOC_FAIL
Dynamic memory allocation failed.
NE_BAD_PARAM
On entry, argument value had an illegal value.
NE_INT
On entry, n=value.
Constraint: n0.
On entry, nmix=value.
Constraint: nmix1.
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_REAL
On entry, sum of weights wgt is not equal to 1.0: sum =value.
NE_REAL_ARRAY_ELEM_CONS
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

None.

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

None.

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