Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly

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NAG[g05lpc] NAG[nag_rngs_von_mises] - Generates a vector of random numbers from a von Mises distribution, seeds and generator number passed explicitly

Calling Sequence

g05lpc(vk, n, x, igen, iseed, 'fail'=fail)

nag_rngs_von_mises(. . .)

Parameters

vk - float;

On entry: , the concentration argument of the required von Mises distribution.

Constraint: . .

n - integer;

On entry: , the number of pseudo-random numbers to be generated.

Constraint: . .

x - Vector(1..dim, datatype=float[8]);

Note: the dimension, dim, of the array x must be at least .

On exit: the pseudo-random numbers from the specified von Mises distribution.

igen - integer;

On entry: must contain the identification number for the generator to be used to return a pseudo-random number and should remain unchanged following initialization by a prior call to one of the functions g05kbc (nag_rngs_init_repeatable) or g05kcc (nag_rngs_init_nonrepeatable).

iseed - Vector(1.., datatype=integer[kernelopts('wordsize')/8]);

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.

'fail'=fail - table; (optional)

The NAG error argument, see the documentation for NagError.

Description

	Purpose
	nag_rngs_von_mises (g05lpc) generates a vector of pseudo-random numbers from a von Mises distribution with concentration argument .

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 and concentration argument kappa, , can be written as:

f(theta) = e^(kappa*cos*theta)/(2*Pi*I[0](kappa))

where is reduced modulo so that and . For very small the distribution is almost the uniform distribution, whereas for all the probability is concentrated at one point.

The variates, , 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 g05kbc (nag_rngs_init_repeatable) (for a repeatable sequence if computed sequentially) or g05kcc (nag_rngs_init_nonrepeatable) (for a non-repeatable sequence) must be called prior to the first call to nag_rngs_von_mises (g05lpc).

	Error Indicators and Warnings
	"NE_BAD_PARAM" On entry, argument had an illegal value. "NE_INT" On entry, . Constraint: . "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 consult NAG for assistance. "NE_REAL" On entry, . Constraint: .

	Accuracy
	Not applicable.

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

Examples

>	vk := 1: n := 5: igen := 1: x := Vector(5, datatype=float[8]): iseed := Vector([1762543, 9324783, 42344, 742355], datatype=integer[kernelopts('wordsize')/8]): NAG:-g05lpc(vk, n, x, igen, iseed):

iseed;

	See Also
	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 g05 Chapter Introduction. NAG Toolbox Overview. NAG Web Site.