g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

# NAG Library Function Documentnag_deviates_landau (g01ftc)

## 1  Purpose

nag_deviates_landau (g01ftc) returns the value of the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function.

## 2  Specification

 #include #include
 double nag_deviates_landau (double x, NagError *fail)

## 3  Description

nag_deviates_landau (g01ftc) evaluates an approximation to the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function given by
 $Ψx=Φ-1x$
(where $\Phi \left(\lambda \right)$ is described in nag_prob_landau (g01etc) and nag_prob_density_landau (g01mtc)), using either linear or quadratic interpolation or rational approximations which mimic the asymptotic behaviour. Further details can be found in Kölbig and Schorr (1984).
It can also be used to generate Landau distributed random numbers in the range $0.

## 4  References

Kölbig K S and Schorr B (1984) A program package for the Landau distribution Comp. Phys. Comm. 31 97–111

## 5  Arguments

1:     xdoubleInput
On entry: the argument $x$ of the function.
Constraint: $0.0<{\mathbf{x}}<1.0$.
2:     failNagError *Input/Output
The NAG error argument (see Section 3.6 in the Essential Introduction).

## 6  Error Indicators and Warnings

NE_INTERNAL_ERROR
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
NE_REAL
On entry, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}<1.0$.
On entry, ${\mathbf{x}}=〈\mathit{\text{value}}〉$.
Constraint: ${\mathbf{x}}>0.0$.

## 7  Accuracy

At least $5-6$ significant digits are correct. Such accuracy is normally considered to be adequate for applications in large scale Monte–Carlo simulations.

None.

## 9  Example

This example evaluates ${\Phi }^{-1}\left(x\right)$ at $x=0.5$, and prints the results.

### 9.1  Program Text

Program Text (g01ftce.c)

### 9.2  Program Data

Program Data (g01ftce.d)

### 9.3  Program Results

Program Results (g01ftce.r)