naginterfaces.library.stat.pdf_​vavilov

naginterfaces.library.stat.pdf_vavilov(x, comm)[source]

pdf_vavilov returns the value of the Vavilov density function .

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

For full information please refer to the NAG Library document for g01mu

https://www.nag.com/numeric/nl/nagdoc_28.4/flhtml/g01/g01muf.html

Parameters
xfloat

The argument of the function.

commdict, communication object

Communication structure.

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

Returns
pdffloat

The value of the Vavilov density function .

Raises
NagValueError
(errno )

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

Notes

pdf_vavilov evaluates an approximation to the Vavilov density function given by

where and , is an arbitrary real constant and

is the exponential integral, and is Euler’s constant.

The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

For values of , the Vavilov distribution can be replaced by the Landau distribution since . For values of , the Vavilov distribution can be replaced by a Gaussian distribution with mean and variance .

References

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