NAG Library Routine Document

G01EEF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     X – REAL (KIND=nag_wp)Input

On entry: $\beta$, the value of the beta variate.

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

2:     A – REAL (KIND=nag_wp)Input

On entry: $a$, the first parameter of the required beta distribution.

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

3:     B – REAL (KIND=nag_wp)Input

On entry: $b$, the second parameter of the required beta distribution.

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

4:     TOL – REAL (KIND=nag_wp)Input

On entry: this parameter is no longer referenced, but is included for backwards compatability.

5:     P – REAL (KIND=nag_wp)Output

On exit: the lower tail probability, $P\left(B\le \beta :a,b\right)$.

6:     Q – REAL (KIND=nag_wp)Output

On exit: the upper tail probability, $P\left(B\ge \beta :a,b\right)$.

7:     PDF – REAL (KIND=nag_wp)Output

On exit: the probability density function, $f\left(B:a,b\right)$.

8:     IFAIL – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output parameters may be useful even if $\mathbf{IFAIL}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

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

$\mathbf{IFAIL}=2$

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

$\mathbf{IFAIL}=4$

X is too far out into the tails for the probability to be evaluated exactly. The results returned are $0$ and $1$ as appropriate. These should be a good approximation to the required solution.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01eefe.f90)

9.2  Program Data

Program Data (g01eefe.d)

9.3  Program Results

Program Results (g01eefe.r)