NAG CL Interface
g05src (dist_​vonmises)

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1 Purpose

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

2 Specification

#include <nag.h>
void  g05src (Integer n, double vk, Integer state[], double x[], NagError *fail)
The function may be called by the names: g05src, nag_rand_dist_vonmises or nag_rand_von_mises.

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:
f(θ)= eκcosθ 2πI0(κ) ,  
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 g05kfc (for a repeatable sequence if computed sequentially) or g05kgc (for a non-repeatable sequence) must be called prior to the first call to 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: n Integer Input
On entry: n, the number of pseudorandom numbers to be generated.
Constraint: n0.
2: vk double Input
On entry: κ, the concentration parameter of the required von Mises distribution.
Constraint: 0.0<vknag_real_largest_number/2.0.
3: state[dim] Integer Communication Array
Note: the dimension, dim, of this array is dictated by the requirements of associated functions that must have been previously called. This array MUST be the same array passed as argument state in the previous call to 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] double Output
On exit: the n pseudorandom numbers from the specified von Mises distribution.
5: fail NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_INVALID_STATE
On entry, state vector has been corrupted or not initialized.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL
On entry, vk0.0 or vk too large: vk=value.

7 Accuracy

Not applicable.

8 Parallelism and Performance

g05src is threaded by NAG for parallel execution in multithreaded implementations of the NAG Library.
Please consult the X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the Users' Note for your implementation for any additional implementation-specific information.

9 Further Comments

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

10 Example

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

10.1 Program Text

Program Text (g05srce.c)

10.2 Program Data

None.

10.3 Program Results

Program Results (g05srce.r)