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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 Φ(λ)$\Phi \left(\lambda \right)$.

Syntax

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

Description

nag_stat_prob_landau (g01et) evaluates an approximation to the Landau distribution function Φ(λ)$\Phi \left(\lambda \right)$ given by
 λ Φ(λ) = ∫ φ(λ)dλ, − ∞
$Φ(λ)=∫-∞λϕ(λ)dλ,$
where φ(λ)$\varphi \left(\lambda \right)$ 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:     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)$\Phi \left(\lambda \right)$, 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_prob_landau_example
x = 0.5;
[result] = nag_stat_prob_landau(x)
```
```

result =

0.3733

```
```function g01et_example
x = 0.5;
[result] = g01et(x)
```
```

result =

0.3733

```