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NAG Toolbox: nag_stat_prob_landau (g01et)

Purpose

nag_stat_prob_landau (g01et) returns the value of the Landau distribution function Φ(λ)Φ(λ).

Syntax

[result] = g01et(x)
[result] = nag_stat_prob_landau(x)

Description

nag_stat_prob_landau (g01et) evaluates an approximation to the Landau distribution function Φ(λ)Φ(λ) given by
λ
Φ(λ) = φ(λ)dλ,
Φ(λ)=-λϕ(λ)dλ,
where φ(λ)ϕ(λ) is described in nag_stat_pdf_landau (g01mt), 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

Parameters

Compulsory Input Parameters

1:     x – double scalar
The argument λλ of the function.

Optional Input Parameters

None.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

1:     result – double scalar
The result of the function.

Error Indicators and Warnings

There are no failure exits from this routine.

Accuracy

At least 77 significant digits are usually correct, but occasionally only 66. Such accuracy is normally considered to be adequate for applications in experimental physics.
Because of the asymptotic behaviour of Φ(λ)Φ(λ), which is of the order of exp[exp(λ)]exp[-exp(-λ)], underflow may occur on some machines when λλ is moderately large and negative.

Further Comments

None.

Example

function nag_stat_prob_landau_example
x = 0.5;
[result] = nag_stat_prob_landau(x)
 

result =

    0.3733


function g01et_example
x = 0.5;
[result] = g01et(x)
 

result =

    0.3733



PDF version (NAG web site, 64-bit version, 64-bit version)
Chapter Contents
Chapter Introduction
NAG Toolbox

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