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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_stat_prob_landau (g01et)

## Purpose

nag_stat_prob_landau (g01et) returns the value of the Landau distribution function $\Phi \left(\lambda \right)$.

## Syntax

[result] = g01et(x)
[result] = nag_stat_prob_landau(x)

## Description

nag_stat_prob_landau (g01et) evaluates an approximation to the Landau distribution function $\Phi \left(\lambda \right)$ given by
 $Φλ=∫-∞λϕλdλ,$
where $\varphi \left(\lambda \right)$ is described in nag_stat_pdf_landau (g01mt), using piecewise approximation by rational functions. Further details can be found in Kölbig and Schorr (1984).

## 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 $\Phi \left(\lambda \right)$, 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 $\Phi \left(\lambda \right)$ at $\lambda =0.5$, and prints the results.
```function g01et_example

fprintf('g01et example results\n\n');

% probability for Landau distribution function
x = 0.5;
[p] = g01et(x);

fprintf('Phi(%5.2f) = %7.4f\n',x,p);

```
```g01et example results

Phi( 0.50) =  0.3733
```