nag_rand_cauchy (g05scc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_cauchy (g05scc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_cauchy (g05scc) 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_rand_cauchy (Integer n, double xmed, double semiqr, Integer state[], double x[], NagError *fail)

3  Description

The distribution has PDF (probability density function)
fx=1πb 1+ x-ab 2 .
nag_rand_cauchy (g05scc) 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_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_cauchy (g05scc).

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:     xmeddoubleInput
On entry: a, the median of the distribution.
3:     semiqrdoubleInput
On entry: b, the semi-interquartile range of the distribution.
Constraint: semiqr0.0.
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 Cauchy 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, semiqr=value.
Constraint: semiqr0.0.

7  Accuracy

Not applicable.

8  Further Comments

None.

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_rand_cauchy (g05scc), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05scce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05scce.r)


nag_rand_cauchy (g05scc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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