nag_rngs_cauchy (g05llc) (PDF version)
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g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rngs_cauchy (g05llc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_cauchy (g05llc) generates a vector of pseudorandom numbers from a Cauchy distribution with median a and semi-interquartile range b.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rngs_cauchy (double xmed, double semiqr, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx=1πb 1+ x-ab 2 .
nag_rngs_cauchy (g05llc) returns the value
a+b2y1- 1y2,
where y1 and y2 are a pair of consecutive pseudorandom numbers from a uniform distribution over 0,1, such that
2y1-1 2+y221.
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_cauchy (g05llc).

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:     xmeddoubleInput
On entry: a, the median of the distribution.
2:     semiqrdoubleInput
On entry: b, the semi-interquartile range of the distribution.
Constraint: semiqr0.0.
3:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
4:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified Cauchy distribution.
5:     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).
6:     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.
7:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

On entry, argument value had an illegal value.
On entry, n=value.
Constraint: n0.
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, semiqr=value.
Constraint: semiqr0.0.

7  Accuracy

Not applicable.

8  Further Comments


9  Example

This example prints the first five pseudorandom real numbers from a Cauchy distribution with median 1.0 and semi-interquartile range 2.0, generated by a single call to nag_rngs_cauchy (g05llc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05llce.c)

9.2  Program Data


9.3  Program Results

Program Results (g05llce.r)

nag_rngs_cauchy (g05llc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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