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Chapter Contents

Chapter Introduction

NAG Toolbox

NAG Toolbox: nag_stat_pdf_landau (g01mt)

▸▿ 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 (g01mt) returns the value of the Landau density function

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)

given by

ϕ (λ) = \frac{1}{2 π i} \int_{c - i \infty}^{c + i \infty} \exp (λ s + s \ln s) d s,

where

c

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)

, 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 $λ$ 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: g01mt_example

function g01mt_example


fprintf('g01mt example results\n\n');

x = 0.5;
[y] = g01mt(x);

fprintf('phi(%5.2f) = %9.4e\n', x, y);

g01mt example results

phi( 0.50) = 1.6523e-01

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Chapter Contents

Chapter Introduction

NAG Toolbox