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Chapter Contents
Chapter Introduction
NAG Toolbox

# NAG Toolbox: nag_stat_pdf_landau_deriv (g01rt)

## Purpose

nag_stat_pdf_landau_deriv (g01rt) returns the value of the derivative φ(λ)${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function.

## Syntax

[result] = g01rt(x)
[result] = nag_stat_pdf_landau_deriv(x)

## Description

nag_stat_pdf_landau_deriv (g01rt) evaluates an approximation to the derivative φ(λ)${\varphi }^{\prime }\left(\lambda \right)$ of the Landau density function given by
 φ′(λ) = (dφ(λ))/(dλ), $ϕ′(λ)=dϕ(λ) dλ ,$
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 φ(λ)$\varphi \left(\lambda \right)$, nag_stat_pdf_landau (g01mt) 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)${\varphi }^{\prime }\left(\lambda \right)$, 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_deriv_example
x = 0.5;
[result] = nag_stat_pdf_landau_deriv(x)
```
```

result =

-0.0360

```
```function g01rt_example
x = 0.5;
[result] = g01rt(x)
```
```

result =

-0.0360

```