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NAG Toolbox: nag_stat_pdf_landau_moment1 (g01pt)

▸▿ Contents

    1  Purpose
    2  Syntax
    3  Description
    4  References
▸▿ 5  Parameters
    6  Error Indicators and Warnings
    7  Accuracy
    8  Further Comments
    9  Example

Purpose

nag_stat_pdf_landau_moment1 (g01pt) returns the value of the first moment Φ1x of the Landau density function.

Syntax

[result] = g01pt(x)
[result] = nag_stat_pdf_landau_moment1(x)

Description

nag_stat_pdf_landau_moment1 (g01pt) evaluates an approximation to the first moment Φ1 x of the Landau density function given by
Φ1x=1Φx ∫-∞xλϕλdλ,  
where ϕλ is described in nag_stat_pdf_landau (g01mt), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).
To obtain the value of Φ2x, nag_stat_pdf_landau_moment2 (g01qt) 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 x 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.

Further Comments

None.

Example

This example evaluates Φ1x at x=0.5, and prints the results.

Open in the MATLAB editor: g01pt_example

function g01pt_example


fprintf('g01pt example results\n\n');

x = 0.5;
[phi1] = g01pt(x);

fprintf('Phi_1(%5.2f) = %8.4f\n', x, phi1);



g01pt example results

Phi_1( 0.50) =  -0.6293
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