NAG Library Routine Document

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 $P\left(B\le \beta :a,b\text{;}\lambda \right)$ 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:     $\mathbf{maxit}$ – IntegerInput

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:     $\mathbf{ifail}$ – IntegerInput/Output

On entry: ifail must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this argument you should refer to Section 3.4 in How to Use the NAG Library and its Documentation 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 arguments 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, $\mathbf{a}=〈\mathit{\text{value}}〉$.
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 3.9 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-399$

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

See Section 3.8 in How to Use the NAG Library and its Documentation for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 3.7 in How to Use the NAG Library and its Documentation for further information.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01gefe.f90)

10.2

Program Data

Program Data (g01gefe.d)

10.3

Program Results

Program Results (g01gefe.r)