naginterfaces.library.stat.inv_​cdf_​landau

naginterfaces.library.stat.inv_cdf_landau(x)

inv_cdf_landau returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

For full information please refer to the NAG Library document for g01ft

https://support.nag.com/numeric/nl/nagdoc_30/flhtml/g01/g01ftf.html

Parameters

xfloat

The argument $x$ of the function.

Returns

invlanfloat

The value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

Raises

NagValueError

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $x<1.0$.

(errno $1$)

On entry, $x=⟨value⟩$.

Constraint: $x>0.0$.

Notes

inv_cdf_landau evaluates an approximation to the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function given by

$$\Psi \left(x\right)={\Phi }^{-1}\left(x\right)$$

(where $\Phi \left(\lambda \right)$ is described in prob_landau() and pdf_landau()), using either linear or quadratic interpolation or rational approximations which mimic the asymptotic behaviour. Further details can be found in Kölbig and Schorr (1984).

It can also be used to generate Landau distributed random numbers in the range $0<x<1$.

References

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