naginterfaces.library.stat.prob_​landau

naginterfaces.library.stat.prob_landau(x)

prob_landau returns the value of the Landau distribution function $\Phi \left(\lambda \right)$.

For full information please refer to the NAG Library document for g01et

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g01/g01etf.html

Parameters

xfloat

The argument $\lambda$ of the function.

Returns

pfloat

The value of the Landau distribution function $\Phi \left(\lambda \right)$.

Notes

prob_landau evaluates an approximation to the Landau distribution function $\Phi \left(\lambda \right)$ given by

$$\Phi \left(\lambda \right)={\int }_{-\infty }^{\lambda }\varphi \left(\lambda \right)d\lambda \text{,}$$

where $\varphi \left(\lambda \right)$ is described in pdf_landau(), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

References

Kölbig, K S and Schorr, B, 1984, A program package for the Landau distribution, Comp. Phys. Comm. (31), 97–111