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Chapter Contents

Chapter Introduction

NAG Toolbox: nag_stat_pdf_landau_moment2 (g01qt)

▸▿ Contents

1 Purpose

2 Syntax

3 Description

4 References

▸▿ 5 Parameters

5.1 Compulsory Input Parameters

5.2 Optional Input Parameters

5.3 Output Parameters

6 Error Indicators and Warnings

7 Accuracy

8 Further Comments

9 Example

Purpose

nag_stat_pdf_landau_moment2 (g01qt) returns the value of the second moment

Φ_{2} (x)

of the Landau density function.

Syntax

[result] = g01qt(x)

[result] = nag_stat_pdf_landau_moment2(x)

Description

nag_stat_pdf_landau_moment2 (g01qt) evaluates an approximation to the second moment

Φ_{2} (x)

of the Landau density function given by

Φ_{2} (x) = \frac{1}{Φ (x)} \int_{- \infty}^{x} λ^{2} ϕ (λ) d λ,

where

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).

To obtain the value of

Φ_{1} (x)

, nag_stat_pdf_landau_moment1 (g01pt) 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

Φ_{2} (x)

at

x = 0.5

, and prints the results.

Open in the MATLAB editor: g01qt_example

function g01qt_example


fprintf('g01qt example results\n\n');

x = 0.5;
[phi2] = g01qt(x);

fprintf('Phi_2(%5.2f) = %8.4f\n', x, phi2);

g01qt example results

Phi_2( 0.50) =   0.9087

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Chapter Contents

Chapter Introduction

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