NAG Library Function Document

nag_prob_vavilov (g01euc)

 Contents

    1  Purpose
    7  Accuracy

1
Purpose

nag_prob_vavilov (g01euc) returns the value of the Vavilov distribution function ΦVλ;κ,β2.
It is intended to be used after a call to nag_init_vavilov (g01zuc).

2
Specification

#include <nag.h>
#include <nagg01.h>
double  nag_prob_vavilov (double x, const double comm_arr[])

3
Description

nag_prob_vavilov (g01euc) evaluates an approximation to the Vavilov distribution function ΦVλ;κ,β2 given by
ΦVλ;κ,β2=-λϕVλ;κ,β2dλ,  
where ϕλ is described in nag_prob_density_vavilov (g01muc). The method used is based on Fourier expansions. Further details can be found in Schorr (1974).

4
References

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

5
Arguments

1:     x doubleInput
On entry: the argument λ of the function.
2:     comm_arr[322] const doubleCommunication Array
On entry: this must be the same argument comm_arr as returned by a previous call to nag_init_vavilov (g01zuc).

6
Error Indicators and Warnings

None.

7
Accuracy

At least five significant digits are usually correct.

8
Parallelism and Performance

nag_prob_vavilov (g01euc) is not threaded in any implementation.

9
Further Comments

nag_prob_vavilov (g01euc) can be called repeatedly with different values of λ provided that the values of κ and β2 remain unchanged between calls. Otherwise, nag_init_vavilov (g01zuc) must be called again. This is illustrated in Section 10.

10
Example

This example evaluates ΦVλ;κ,β2 at λ=0.1, κ=2.5 and β2=0.7, and prints the results.

10.1
Program Text

Program Text (g01euce.c)

10.2
Program Data

Program Data (g01euce.d)

10.3
Program Results

Program Results (g01euce.r)

© The Numerical Algorithms Group Ltd, Oxford, UK. 2017