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Chapter Introduction
NAG Toolbox

NAG Toolbox: nag_stat_prob_vavilov (g01eu)


    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example


nag_stat_prob_vavilov (g01eu) returns the value of the Vavilov distribution function ΦVλ;κ,β2.
It is intended to be used after a call to nag_stat_init_vavilov (g01zu).


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


nag_stat_prob_vavilov (g01eu) evaluates an approximation to the Vavilov distribution function ΦVλ;κ,β2 given by
where ϕλ is described in nag_stat_pdf_vavilov (g01mu). The method used is based on Fourier expansions. Further details can be found in Schorr (1974).


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


Compulsory Input Parameters

1:     x – double scalar
The argument λ of the function.
2:     rcomm322 – double array
This must be the same argument rcomm as returned by a previous call to nag_stat_init_vavilov (g01zu).

Optional Input Parameters


Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
Either the initialization function has not been called prior to the first call of this function or a communication array has become corrupted.
An unexpected error has been triggered by this routine. Please contact NAG.
Your licence key may have expired or may not have been installed correctly.
Dynamic memory allocation failed.


At least five significant digits are usually correct.

Further Comments

nag_stat_prob_vavilov (g01eu) can be called repeatedly with different values of λ provided that the values of κ and β2 remain unchanged between calls. Otherwise, nag_stat_init_vavilov (g01zu) must be called again. This is illustrated in Example.


This example evaluates ΦVλ;κ,β2 at λ=0.1, κ=2.5 and β2=0.7, and prints the results.
function g01eu_example

fprintf('g01eu example results\n\n');

% Vavilov distribution function
rkappa = 2.5;
beta2 = 0.7;
mode = int64(1);
x = 0.1;

[xl, xu, work, ifail] = g01zu( ...
			       rkappa, beta2, mode);

[p, ifail] = g01eu(x, work);

fprintf('Phi_v(%5.1f;%5.1f,%6.2f) = %7.4f\n',x,rkappa,beta2,p);

g01eu example results

Phi_v(  0.1;  2.5,  0.70) =  0.9998

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Chapter Introduction
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