naginterfaces.library.rand.dist_​vonmises

naginterfaces.library.rand.dist_vonmises(n, vk, statecomm)

dist_vonmises generates a vector of pseudorandom numbers from a von Mises distribution with concentration parameter $\kappa$.

For full information please refer to the NAG Library document for g05sr

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g05/g05srf.html

Parameters

nint

$n$, the number of pseudorandom numbers to be generated.

vkfloat

$\kappa$, the concentration parameter of the required von Mises distribution.

statecommdict, RNG communication object, modified in place

RNG communication structure.

This argument must have been initialized by a prior call to init_repeat() or init_nonrepeat().

Returns

xfloat, ndarray, shape $\left(n\right)$

The $n$ pseudorandom numbers from the specified von Mises distribution.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 0$.

(errno $2$)

On entry, $vk\le 0.0$ or $vk$ too large: $vk=⟨value⟩$.

(errno $3$)

On entry, $statecomm$[‘state’] vector has been corrupted or not initialized.

Notes

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 ${\mu }_0=0$ and concentration parameter $\kappa$, can be written as:

$$f\left(\theta \right)=\frac{e^{\kappa \cos \left(\theta \right)}}{2\pi I_0\left(\kappa \right)}\text{,}$$

where $\theta$ is reduced modulo $2\pi$ so that $-\pi \le \theta <\pi$ and $\kappa \ge 0$. For very small $\kappa$ the distribution is almost the uniform distribution, whereas for $\kappa \to \infty$ all the probability is concentrated at one point.

The $n$ variates, ${\theta }_1,{\theta }_2,\dots ,{\theta }_n$, 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 init_repeat() (for a repeatable sequence if computed sequentially) or init_nonrepeat() (for a non-repeatable sequence) must be called prior to the first call to dist_vonmises.

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