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
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.
Best D J and Fisher N I (1979) Efficient simulation of the von Mises distribution Appl. Statist. 28 152–157
Not applicable.
Background information to multithreading can be found in the
Multithreading documentation.
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
g05src, after initialization by
g05kfc.
None.