NAG Toolbox: nag_stat_inv_cdf_beta (g01fe)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{p}$ – double scalar

$p$, the lower tail probability from the required beta distribution.

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

2:     $\mathrm{a}$ – double scalar

$a$, the first parameter of the required beta distribution.

Constraint: $0.0<\mathbf{a}\le {10}^6$.

3:     $\mathrm{b}$ – double scalar

$b$, the second parameter of the required beta distribution.

Constraint: $0.0<\mathbf{b}\le {10}^6$.

Optional Input Parameters

1:     $\mathrm{tol}$ – double scalar

Default: $0.0$

The relative accuracy required by you in the result. If nag_stat_inv_cdf_beta (g01fe) is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see nag_machine_precision (x02aj)), then the value of $10\times \mathit{machine precision}$ is used instead.

Output Parameters

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

The result of the function.

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

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

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

   $\mathbf{ifail}=1$

On entry,	$\mathbf{p}<0.0$,
or	$\mathbf{p}>1.0$.

   $\mathbf{ifail}=2$

On entry,	$\mathbf{a}\le 0.0$,
or	$\mathbf{a}>{10}^6$,
or	$\mathbf{b}\le 0.0$,
or	$\mathbf{b}>{10}^6$.

W  $\mathbf{ifail}=3$

There is doubt concerning the accuracy of the computed result. $100$ iterations of the Newton–Raphson method have been performed without satisfying the accuracy criterion (see Accuracy). The result should be a reasonable approximation of the solution.

W  $\mathbf{ifail}=4$

Requested accuracy not achieved when calculating beta probability. The result should be a reasonable approximation to the correct solution. You should try setting tol larger.

   $\mathbf{ifail}=-99$

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: g01fe_example

function g01fe_example


fprintf('g01fe example results\n\n');

p = [    0.50    0.99    0.25];
a = [    1.0     1.5    20.0 ];
b = [    2.0     1.5    10.0 ];
dev  = p;

fprintf('     p       a       b    deviate\n');
for j = 1:numel(p)
   [dev(j), ifail] = g01fe( ...
			    p(j), a(j), b(j));
end

fprintf('%8.3f%8.3f%8.3f%8.3f\n', [p; a; b; dev]);

g01fe example results

     p       a       b    deviate
   0.500   1.000   2.000   0.293
   0.990   1.500   1.500   0.967
   0.250  20.000  10.000   0.611