naginterfaces.library.stat.pdf_​landau_​moment2

naginterfaces.library.stat.pdf_landau_moment2(x)

pdf_landau_moment2 returns the value of the second moment ${\Phi }_2\left(x\right)$ of the Landau density function.

For full information please refer to the NAG Library document for g01qt

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g01/g01qtf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

mom2float

The value of the second moment ${\Phi }_2\left(x\right)$ of the Landau density function.

Notes

pdf_landau_moment2 evaluates an approximation to the second moment ${\Phi }_2\left(x\right)$ of the Landau density function given by

$${\Phi }_2\left(x\right)=\frac{1}{\Phi \left(x\right)}{\int }_{-\infty }^x{\lambda }^2\varphi \left(\lambda \right)d\lambda \text{,}$$

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).

To obtain the value of ${\Phi }_1\left(x\right)$, pdf_landau_moment1() can be used.

References

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