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
and concentration parameter
, can be written as:
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
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).
Best D J and Fisher N I (1979) Efficient simulation of the von Mises distribution Appl. Statist. 28 152–157
Not applicable.
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.
For a given number of random variates the generation time increases slightly with increasing .
This example prints the first five pseudorandom numbers from a von Mises distribution with
, generated by a single call to
nag_rand_von_mises (g05src), after initialization by
nag_rand_init_repeatable (g05kfc).
None.