NAG Toolbox: nag_stat_prob_beta_noncentral (g01ge)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{x}$ – double scalar

$\beta$, the deviate from the beta distribution, for which the probability $P\left(B\le \beta :a,b\text{;}\lambda \right)$ is to be found.

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

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

4:     $\mathrm{rlamda}$ – double scalar

$\lambda$, the noncentrality parameter of the required beta distribution.

Constraint: $0.0\le \mathbf{rlamda}\le -2.0\log \left(U\right)$, where $U$ is the safe range parameter as defined by nag_machine_real_safe (x02am).

Optional Input Parameters

1:     $\mathrm{tol}$ – double scalar

Default: $0.0$

The relative accuracy required by you in the results. If nag_stat_prob_beta_noncentral (g01ge) 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.

See Accuracy for the relationship between tol and maxit.

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

Default: $500$.

The maximum number of iterations that the algorithm should use.

See Accuracy for suggestions as to suitable values for maxit for different values of the arguments.

Constraint: $\mathbf{maxit}\ge 1$.

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,	$\mathbf{a}\le 0.0$,
or	$\mathbf{a}>{10}^6$,
or	$\mathbf{b}\le 0.0$,
or	$\mathbf{b}>{10}^6$,
or	$\mathbf{rlamda}<0.0$,
or	$\mathbf{rlamda}>-2.0\log \left(U\right)$, where $U=$ safe range argument as defined by nag_machine_real_safe (x02am),
or	$\mathbf{x}<0.0$,
or	$\mathbf{x}>1.0$,
or	$\mathbf{maxit}<1$.

If on exit $\mathbf{ifail}=\mathbf{1}$ then nag_stat_prob_beta_noncentral (g01ge) returns zero.

W  $\mathbf{ifail}=2$

The solution has failed to converge in maxit iterations. You should try a larger value of maxit or tol. The returned value will be an approximation to the correct value.

W  $\mathbf{ifail}=3$

The probability is too close to $0.0$ or $1.0$ for the algorithm to be able to calculate the required probability. nag_stat_prob_beta_noncentral (g01ge) will return $0.0$ or $1.0$ as appropriate, this should be a reasonable approximation.

W  $\mathbf{ifail}=4$

The required accuracy was not achieved when calculating the initial value of $P\left(B\le \beta :a,b\text{;}\lambda \right)$. You should try a larger value of tol. The returned value will be an approximation to the correct value.

   $\mathbf{ifail}=-99$

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: g01ge_example

function g01ge_example


fprintf('g01ge example results\n\n');

x      = [ 0.25   0.75   0.5];
a      = [ 1      1.5    2  ];
b      = [ 2      1.5    1  ];
rlamda = [ 1      0.5    0  ];
p      = x;

fprintf('     x       a       b     rlamda    p\n');
for j = 1:numel(x)
   [p(j), ifail] = g01ge( ...
			  x(j), a(j), b(j), rlamda(j));
end

fprintf('%8.3f%8.3f%8.3f%8.3f%8.4f\n', [x; a; b; rlamda; p]);

g01ge example results

     x       a       b     rlamda    p
   0.250   1.000   2.000   1.000  0.3168
   0.750   1.500   1.500   0.500  0.7705
   0.500   2.000   1.000   0.000  0.2500