nag_rngs_von_mises (g05lpc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

NAG Library Function Document

nag_rngs_von_mises (g05lpc)

+ Contents

    1  Purpose
    7  Accuracy

1  Purpose

nag_rngs_von_mises (g05lpc) 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_rngs_von_mises (double vk, Integer n, double x[], Integer igen, Integer iseed[], NagError *fail)

3  Description

The von Mises distribution is a symmetric distribution used in the analysis of circular data. The probability density function of this distribution on the circle with mean direction μ0=0 and concentration parameter kappa, 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_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_von_mises (g05lpc).

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:     vkdoubleInput
On entry: κ, the concentration parameter of the required von Mises distribution.
Constraint: vk>0.0.
2:     nIntegerInput
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     x[n]doubleOutput
On exit: the n pseudorandom numbers from the specified von Mises distribution.
4:     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).
5:     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.
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_REAL
On entry, vk=value.
Constraint: vk>0.0.

7  Accuracy

Not applicable.

8  Further Comments

For a given number of random variates the generation time increases slightly with increasing κ.
If vk is supplied too large (i.e., vk>nag_real_largest_number) then floating point overflow will occur in internal calculation.

9  Example

This example prints the first five pseudorandom real numbers from a von Mises distribution with κ=1.0, generated by a single call to nag_rngs_von_mises (g05lpc), after initialization by nag_rngs_init_repeatable (g05kbc).

9.1  Program Text

Program Text (g05lpce.c)

9.2  Program Data

None.

9.3  Program Results

Program Results (g05lpce.r)


nag_rngs_von_mises (g05lpc) (PDF version)
g05 Chapter Contents
g05 Chapter Introduction
NAG C Library Manual

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