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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_stat_pdf_landau_moment2 (g01qt)

## Purpose

nag_stat_pdf_landau_moment2 (g01qt) returns the value of the second moment Φ2(x)${\Phi }_{2}\left(x\right)$ of the Landau density function.

## Syntax

[result] = g01qt(x)
[result] = nag_stat_pdf_landau_moment2(x)

## Description

nag_stat_pdf_landau_moment2 (g01qt) evaluates an approximation to the second moment Φ2 (x)${\Phi }_{2}\left(x\right)$ of the Landau density function given by
 x Φ2(x) = 1/(Φ(x)) ∫ λ2φ(λ)dλ, − ∞
$Φ2(x)=1Φ(x) ∫-∞xλ2ϕ(λ)dλ,$
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).
To obtain the value of Φ1(x)${\Phi }_{1}\left(x\right)$, nag_stat_pdf_landau_moment1 (g01pt) 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 x$x$ 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.

None.

## Example

```function nag_stat_pdf_landau_moment2_example
x = 0.5;
[result] = nag_stat_pdf_landau_moment2(x)
```
```

result =

0.9087

```
```function g01qt_example
x = 0.5;
[result] = g01qt(x)
```
```

result =

0.9087

```