naginterfaces.library.stat.pdf_​landau_​deriv

naginterfaces.library.stat.pdf_landau_deriv(x)

pdf_landau_deriv returns the value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

For full information please refer to the NAG Library document for g01rt

https://www.nag.com/numeric/nl/nagdoc_29.3/flhtml/g01/g01rtf.html

Parameters

xfloat

The argument $\lambda$ of the function.

Returns

derivfloat

The value of the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

Notes

pdf_landau_deriv evaluates an approximation to the derivative ${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function given by

$${\varphi }^{\prime }\left(\lambda \right)=\frac{d\varphi \left(\lambda \right)}{d\lambda }\text{,}$$

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 $\varphi \left(\lambda \right)$, pdf_landau() can be used.

References

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