NAG Toolbox: nag_stat_init_vavilov (g01zu)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{rkappa}$ – double scalar

The argument $\kappa$ of the function.

Constraint: $0.01\le \mathbf{rkappa}\le 10.0$.

2:     $\mathrm{beta2}$ – double scalar

The argument ${\beta }^2$ of the function.

Constraint: $0.0\le \mathbf{beta2}\le 1.0$.

3:     $\mathrm{mode}$ – int64int32nag_int scalar

If $\mathbf{mode}=0$, then nag_stat_pdf_vavilov (g01mu) is to be called after the call to nag_stat_init_vavilov (g01zu). Otherwise, nag_stat_prob_vavilov (g01eu) is to be called.

Optional Input Parameters

None.

Output Parameters

1:     $\mathrm{xl}$ – double scalar

$x_l$, a threshold value below which ${\varphi }_V\left(\lambda \text{;}\kappa ,{\beta }^2\right)$ will be set to zero by nag_stat_pdf_vavilov (g01mu) and ${\Phi }_V\left(\lambda \text{;}\kappa ,{\beta }^2\right)$ will be set to zero by nag_stat_prob_vavilov (g01eu) if $\lambda <x_l$.

2:     $\mathrm{xu}$ – double scalar

$x_u$, a threshold value above which ${\varphi }_V\left(\lambda \text{;}\kappa ,{\beta }^2\right)$ will be set to zero by nag_stat_pdf_vavilov (g01mu) and ${\Phi }_V\left(\lambda \text{;}\kappa ,{\beta }^2\right)$ will be set to unity by nag_stat_prob_vavilov (g01eu) if $\lambda >x_u$.

3:     $\mathrm{rcomm}\left(322\right)$ – double array

This argument should be passed unchanged to nag_stat_prob_vavilov (g01eu) or nag_stat_pdf_vavilov (g01mu).

4:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

   $\mathbf{ifail}=1$

On entry,	$\mathbf{rkappa}<0.01$,
or	$\mathbf{rkappa}>10.0$,
or	$\mathbf{beta2}<0.0$,
or	$\mathbf{beta2}>1.0$.

   $\mathbf{ifail}=2$

The initialization has been abandoned due to an internal error. This error exit is unlikely to occur, but if it does change the values of rkappa and/or beta2 and rerun nag_stat_init_vavilov (g01zu).

   $\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

   $\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g01zu_example

function g01zu_example


fprintf('g01zu example results\n\n');

x      = 2.5;
rkappa = 0.4;
beta2  = 0.1;

fprintf('  x     rkappa    beta2        y\n\n');

% Initialize rcomm array (new value of rkappa or beta2)
mode = int64(0);
[xl, xu, rcomm, ifail] = g01zu( ...
                               rkappa, beta2, mode);

% Compute value of Vavilov density function
[y, ifail] = g01mu( ...
                    x, rcomm);

% Display results
fprintf('%4.1f%9.1f%9.1f%15.4e\n', x, rkappa, beta2, y);

g01zu example results

  x     rkappa    beta2        y

 2.5      0.4      0.1     8.3675e-02