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 $λ$ of the function.

Optional Input Parameters

None.

Output Parameters

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

Error Indicators and Warnings

None.

Accuracy

At least

7

significant digits are usually correct, but occasionally only

6

. Such accuracy is normally considered to be adequate for applications in experimental physics.

Because of the asymptotic behaviour of

Φ (λ)

, which is of the order of

\exp [- \exp (- λ)]

, underflow may occur on some machines when

λ

is moderately large and negative.

Further Comments

None.

Example

This example evaluates

Φ (λ)

λ = 0.5

, and prints the results.

Open in the MATLAB editor: g01et_example

function g01et_example


fprintf('g01et example results\n\n');

% probability for Landau distribution function
x = 0.5;
[p] = g01et(x);

fprintf('Phi(%5.2f) = %7.4f\n',x,p);

g01et example results

Phi( 0.50) =  0.3733

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox