NAG FL Interface
g01eef (prob_​beta)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{x}$ – Real (Kind=nag_wp) Input

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

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

2: $\mathbf{a}$ – 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: $\mathbf{b}$ – 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: $\mathbf{tol}$ – Real (Kind=nag_wp) Input

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

5: $\mathbf{p}$ – Real (Kind=nag_wp) Output

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

6: $\mathbf{q}$ – Real (Kind=nag_wp) Output

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

7: $\mathbf{pdf}$ – Real (Kind=nag_wp) Output

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

8: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $-1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $-1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $-1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $-1$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ or $\mathbf{1}$ 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, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\le 1.0$.

On entry, $\mathbf{x}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{x}\ge 0.0$.

$\mathbf{ifail}=2$

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{a}>0.0$.

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{b}>0.0$.

$\mathbf{ifail}=-99$

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

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

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

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results