nag_prob_vavilov (g01euc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

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:     xdoubleInput
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  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 9.

9  Example

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

9.1  Program Text

Program Text (g01euce.c)

9.2  Program Data

Program Data (g01euce.d)

9.3  Program Results

Program Results (g01euce.r)


nag_prob_vavilov (g01euc) (PDF version)
g01 Chapter Contents
g01 Chapter Introduction
NAG C Library Manual

© The Numerical Algorithms Group Ltd, Oxford, UK. 2012