nag_rand_von_mises (g05src) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rand_von_mises (g05src)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rand_von_mises (g05src) generates a vector of pseudorandom numbers from a von Mises distribution with concentration parameter κ.

2  Specification

#include <nag.h>
#include <nagg05.h>
void  nag_rand_von_mises (Integer n, double vk, Integer state[], double x[], NagError *fail)

3  Description

The von Mises distribution is a symmetric distribution used in the analysis of circular data. The PDF (probability density function) of this distribution on the circle with mean direction μ0=0 and concentration parameter κ, can be written as:
fθ= eκcosθ 2πI0κ ,
where θ is reduced modulo 2π so that -πθ<π and κ0. For very small κ the distribution is almost the uniform distribution, whereas for κ all the probability is concentrated at one point.
The n variates, θ1,θ2,,θn, are generated using an envelope rejection method with a wrapped Cauchy target distribution as proposed by Best and Fisher (1979) and described by Dagpunar (1988).
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_von_mises (g05src).

4  References

Best D J and Fisher N I (1979) Efficient simulation of the von Mises distribution Appl. Statist. 28 152–157
Dagpunar J (1988) Principles of Random Variate Generation Oxford University Press
Mardia K V (1972) Statistics of Directional Data Academic Press

5  Arguments

1:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2:     vkdoubleInput
On entry: κ, the concentration parameter of the required von Mises distribution.
Constraint: 0.0<vknag_real_largest_number/2.0.
3:     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.
4:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified von Mises distribution.
5:     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, vk0.0 or vk too large: vk=value.

7  Accuracy

Not applicable.

8  Further Comments

For a given number of random variates the generation time increases slightly with increasing κ.

9  Example

This example prints the first five pseudorandom numbers from a von Mises distribution with κ=1.0, generated by a single call to nag_rand_von_mises (g05src), after initialization by nag_rand_init_repeatable (g05kfc).

9.1  Program Text

Program Text (g05srce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05srce.r)


nag_rand_von_mises (g05src) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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