NAG FL Interface
g01gef (prob_​beta_​noncentral)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

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

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

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

On entry: $\lambda$, 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 x02amf.

5: $\mathbf{tol}$ – Real (Kind=nag_wp) Input

On entry: the relative accuracy required by you in the results. If g01gef is entered with tol greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see x02ajf), the value of $10\times \mathit{machine precision}$ is used instead.

See Section 7 for the relationship between tol and maxit.

6: $\mathbf{maxit}$ – Integer Input

On entry: the maximum number of iterations that the algorithm should use.

See Section 7 for suggestions as to suitable values for maxit for different values of the arguments.

Suggested value: $500$.

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

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

On entry: ifail must be set to $0$, $\mathrm{-1}$ 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 $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $\mathrm{-1}$ 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, $\mathbf{a}=⟨\mathit{\text{value}}⟩$.
Constraint: $0.0<\mathbf{a}\le {10}^6$.

On entry, $\mathbf{b}=⟨\mathit{\text{value}}⟩$.
Constraint: $0.0<\mathbf{b}\le {10}^6$.

On entry, $\mathbf{maxit}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{maxit}\ge 1$.

On entry, $\mathbf{rlamda}=⟨\mathit{\text{value}}⟩$.
Constraint: $0.0\le \mathbf{rlamda}\le -2.0\log \left(U\right)$, where $U$ is the safe range parameter as defined by x02amf.

On entry, $\mathbf{x}=⟨\mathit{\text{value}}⟩$.
Constraint: $0.0\le \mathbf{x}\le 1.0$.

$\mathbf{ifail}=2$

The solution has failed to converge in $⟨\mathit{\text{value}}⟩$ iterations. Consider increasing maxit or tol. The returned value will be an approximation to the correct value.

$\mathbf{ifail}=3$

The probability is too close to $0.0$ or $1.0$ for the algorithm to be able to calculate the required probability. g01gef will return $0.0$ or $1.0$ as appropriate. This should be a reasonable approximation.

$\mathbf{ifail}=4$

The required accuracy was not achieved when calculating the initial value of the beta distribution. You should try a larger value of tol. The returned value will be an approximation to the correct value. This error exit is no longer possible but is still documented for historical reasons.

$\mathbf{ifail}=-99$

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