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# NAG Toolbox: nag_stat_pdf_landau (g01mt)

## Purpose

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

## Syntax

[result] = g01mt(x)
[result] = nag_stat_pdf_landau(x)

## Description

nag_stat_pdf_landau (g01mt) evaluates an approximation to the Landau density function $\varphi \left(\lambda \right)$ given by
 $ϕλ=12πi ∫c-i∞ c+i∞expλs+sln⁡sds,$
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 ${\varphi }^{\prime }\left(\lambda \right)$, 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:     $\mathrm{x}$ – double scalar
The argument $\lambda$ of the function.

None.

### Output Parameters

1:     $\mathrm{result}$ – double scalar
The result of the function.

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 $\varphi \left(\lambda \right)$, which is of the order of $\mathrm{exp}\left[-\mathrm{exp}\left(-\lambda \right)\right]$, underflow may occur on some machines when $\lambda$ is moderately large and negative.

None.

## Example

This example evaluates $\varphi \left(\lambda \right)$ at $\lambda =0.5$, and prints the results.
```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

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