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Chapter Contents
Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_stat_pdf_landau (g01mt)

Purpose

nag_stat_pdf_landau (g01mt) returns the value of the Landau density function φ(λ)$\varphi \left(\lambda \right)$.

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)$\varphi \left(\lambda \right)$ given by
 c + i∞ φ(λ) = 1/(2πi) ∫ exp(λs + slns)ds, c − i∞
$ϕ(λ)=12πi ∫c-i∞ c+i∞exp(λs+sln⁡s)ds,$
where c$c$ 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)${\varphi }^{\prime }\left(\lambda \right)$, 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$\lambda$ of the function.

None.

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 7$7$ significant digits are usually correct, but occasionally only 6$6$. Such accuracy is normally considered to be adequate for applications in experimental physics.
Because of the asymptotic behaviour of φ(λ)$\varphi \left(\lambda \right)$, which is of the order of exp[exp(λ)]$\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when λ$\lambda$ is moderately large and negative.

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

```