naginterfaces.library.stat.prob_​vavilov

naginterfaces.library.stat.prob_vavilov(x, comm)

prob_vavilov returns the value of the Vavilov distribution function ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$.

It is intended to be used after a call to init_vavilov().

For full information please refer to the NAG Library document for g01eu

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g01/g01euf.html

Parameters

xfloat

The argument $\lambda$ of the function.

commdict, communication object

Communication structure.

This argument must have been initialized by a prior call to init_vavilov().

Returns

pfloat

The value of the Vavilov distribution function ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$.

Raises

NagValueError

(errno $1$)

Either the initialization function has not been called prior to the first call of this function or a communication array has become corrupted.

Notes

prob_vavilov evaluates an approximation to the Vavilov distribution function ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ given by

$${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)={\int }_{-\infty }^{\lambda }{\varphi }_V(\lambda \text{;}\kappa ,{\beta }^2)d\lambda \text{,}$$

where $\varphi \left(\lambda \right)$ is described in pdf_vavilov(). The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

References

Schorr, B, 1974, Programs for the Landau and the Vavilov distributions and the corresponding random numbers, Comp. Phys. Comm. (7), 215–224