# NAG CL Interfaceg01ftc (inv_​cdf_​landau)

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## 1Purpose

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

## 2Specification

 #include
 double g01ftc (double x, NagError *fail)
The function may be called by the names: g01ftc, nag_stat_inv_cdf_landau or nag_deviates_landau.

## 3Description

g01ftc evaluates an approximation to the inverse ${\Phi }^{-1}\left(x\right)$ of the Landau distribution function given by
 $Ψ(x)=Φ-1(x)$
(where $\Phi \left(\lambda \right)$ is described in g01etc and 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.

## 4References

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

## 5Arguments

1: $\mathbf{x}$double Input
On entry: the argument $x$ of the function.
Constraint: $0.0<{\mathbf{x}}<1.0$.
2: $\mathbf{fail}$NagError * Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

## 6Error Indicators and Warnings

NE_ALLOC_FAIL
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
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.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL
On entry, ${\mathbf{x}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{x}}<1.0$.
On entry, ${\mathbf{x}}=⟨\mathit{\text{value}}⟩$.
Constraint: ${\mathbf{x}}>0.0$.

## 7Accuracy

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

## 8Parallelism and Performance

g01ftc is not threaded in any implementation.

None.

## 10Example

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

### 10.1Program Text

Program Text (g01ftce.c)

### 10.2Program Data

Program Data (g01ftce.d)

### 10.3Program Results

Program Results (g01ftce.r)