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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)ΦV(λ;κ,β2).
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)ΦV(λ;κ,β2) given by
λ
ΦV(λ;κ,β2) = φV(λ;κ,β2)dλ,
ΦV(λ;κ,β2)=-λϕV(λ;κ,β2)dλ,
where φ(λ)ϕ(λ) 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 λλ of the function.
2:     rcomm(322322) – double array
This must be the same parameter rcomm as returned by a previous call to nag_stat_init_vavilov (g01zu).

Optional Input Parameters

None.

Input Parameters Omitted from the MATLAB Interface

None.

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=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.

Further Comments

nag_stat_prob_vavilov (g01eu) can be called repeatedly with different values of λλ provided that the values of κκ and β2β2 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
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