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# NAG Toolbox: nag_stat_prob_vavilov (g01eu)

## Purpose

nag_stat_prob_vavilov (g01eu) returns the value of the Vavilov distribution function ΦV(λ;κ,β2)${\Phi }_{V}\left(\lambda \text{;}\kappa ,{\beta }^{2}\right)$.
It is intended to be used after a call to nag_stat_init_vavilov (g01zu).

## Syntax

[result, ifail] = g01eu(x, rcomm)
[result, ifail] = nag_stat_prob_vavilov(x, rcomm)

## Description

nag_stat_prob_vavilov (g01eu) evaluates an approximation to the Vavilov distribution function ΦV(λ;κ,β2)${\Phi }_{V}\left(\lambda \text{;}\kappa ,{\beta }^{2}\right)$ given by
 λ ΦV(λ;κ,β2) = ∫ φV(λ;κ,β2)dλ, − ∞
$ΦV(λ;κ,β2)=∫-∞λϕV(λ;κ,β2)dλ,$
where φ(λ)$\varphi \left(\lambda \right)$ is described in nag_stat_pdf_vavilov (g01mu). The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

## References

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

## Parameters

### Compulsory Input Parameters

1:     x – double scalar
The argument λ$\lambda$ of the function.
2:     rcomm(322$322$) – double array
This must be the same parameter rcomm as returned by a previous call to nag_stat_init_vavilov (g01zu).

None.

None.

### Output Parameters

1:     result – double scalar
The result of the function.
2:     ifail – int64int32nag_int scalar
${\mathrm{ifail}}={\mathbf{0}}$ unless the function detects an error (see [Error Indicators and Warnings]).

## Error Indicators and Warnings

Errors or warnings detected by the function:
ifail = 1${\mathbf{ifail}}=1$
Either the initialization function has not been called prior to the first call of this function or a communication array has become corrupted.

## Accuracy

At least five significant digits are usually correct.

nag_stat_prob_vavilov (g01eu) can be called repeatedly with different values of λ$\lambda$ provided that the values of κ$\kappa$ and β2${\beta }^{2}$ remain unchanged between calls. Otherwise, nag_stat_init_vavilov (g01zu) must be called again. This is illustrated in Section [Example].

## Example

```function nag_stat_prob_vavilov_example
rkappa = 2.5;
beta2 = 0.7;
mode = int64(1);
x = 0.1;
[xl, xu, work, ifail] = nag_stat_init_vavilov(rkappa, beta2, mode);
[result, ifail] = nag_stat_prob_vavilov(x, work)
```
```

result =

0.9998

ifail =

0

```
```function g01eu_example
rkappa = 2.5;
beta2 = 0.7;
mode = int64(1);
x = 0.1;
[xl, xu, work, ifail] = g01zu(rkappa, beta2, mode);
[result, ifail] = g01eu(x, work)
```
```

result =

0.9998

ifail =

0

```

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Chapter Introduction
NAG Toolbox

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