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NAG Toolbox: nag_stat_pdf_landau (g01mt)

Purpose

nag_stat_pdf_landau (g01mt) returns the value of the Landau density function φ(λ)ϕ(λ).

Syntax

[result] = g01mt(x)
[result] = nag_stat_pdf_landau(x)

Description

nag_stat_pdf_landau (g01mt) evaluates an approximation to the Landau density function φ(λ)ϕ(λ) given by
c + i
φ(λ) = 1/(2πi)exp(λs + slns)ds,
ci
ϕ(λ)=12πi c-i c+iexp(λs+slns)ds,
where cc 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 φ(λ)ϕ(λ), nag_stat_pdf_landau_deriv (g01rt) can be used.

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_pdf_landau_example
x = 0.5;
[result] = nag_stat_pdf_landau(x)
 

result =

    0.1652


function g01mt_example
x = 0.5;
[result] = g01mt(x)
 

result =

    0.1652



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

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