# NAG CL Interfaceg01euc (prob_​vavilov)

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## 1Purpose

g01euc returns the value of the Vavilov distribution function ${\Phi }_{V}\left(\lambda \text{;}\kappa ,{\beta }^{2}\right)$.
It is intended to be used after a call to g01zuc.

## 2Specification

 #include
 double g01euc (double x, const double comm_arr[])
The function may be called by the names: g01euc, nag_stat_prob_vavilov or nag_prob_vavilov.

## 3Description

g01euc evaluates an approximation to the Vavilov distribution function ${\Phi }_{V}\left(\lambda \text{;}\kappa ,{\beta }^{2}\right)$ given by
 $ΦV(λ;κ,β2)=∫-∞λϕV(λ;κ,β2)dλ,$
where $\varphi \left(\lambda \right)$ is described in g01muc. The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

## 4References

Schorr B (1974) Programs for the Landau and the Vavilov distributions and the corresponding random numbers Comp. Phys. Comm. 7 215–224

## 5Arguments

1: $\mathbf{x}$double Input
On entry: the argument $\lambda$ of the function.
2: $\mathbf{comm_arr}\left[322\right]$const double Communication Array
On entry: this must be the same argument comm_arr as returned by a previous call to g01zuc.

None.

## 7Accuracy

At least five significant digits are usually correct.

## 8Parallelism and Performance

g01euc is not threaded in any implementation.

g01euc can be called repeatedly with different values of $\lambda$ provided that the values of $\kappa$ and ${\beta }^{2}$ remain unchanged between calls. Otherwise, g01zuc must be called again. This is illustrated in Section 10.

## 10Example

This example evaluates ${\Phi }_{V}\left(\lambda \text{;}\kappa ,{\beta }^{2}\right)$ at $\lambda =0.1$, $\kappa =2.5$ and ${\beta }^{2}=0.7$, and prints the results.

### 10.1Program Text

Program Text (g01euce.c)

### 10.2Program Data

Program Data (g01euce.d)

### 10.3Program Results

Program Results (g01euce.r)