naginterfaces.library.stat.pdf_​landau

naginterfaces.library.stat.pdf_landau(x)

pdf_landau returns the value of the Landau density function $\varphi \left(\lambda \right)$.

For full information please refer to the NAG Library document for g01mt

https://support.nag.com/numeric/nl/nagdoc_30.1/flhtml/g01/g01mtf.html

Parameters

xfloat

The argument $\lambda$ of the function.

Returns

pdffloat

The value of the Landau density function $\varphi \left(\lambda \right)$.

Notes

pdf_landau evaluates an approximation to the Landau density function $\varphi \left(\lambda \right)$ given by

$$\varphi \left(\lambda \right)=\frac{1}{2\pi i}{\int }_{c-i\infty }^{c+i\infty }exp(\lambda s+sln\left(s\right))ds\text{,}$$

where $c$ is an arbitrary real constant, using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

To obtain the value of ${\varphi }^{\prime }\left(\lambda \right)$, pdf_landau_deriv() can be used.

References

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