NAG Library Routine Document

g01fef  (inv_cdf_beta)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

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

On entry: $p$, the lower tail probability from the required beta distribution.

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

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: the relative accuracy required by you in the result. If g01fef 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.

5:     $\mathbf{ifail}$ – 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, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}\le 1.0$.

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

$\mathbf{ifail}=2$

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: $\mathbf{a}\le {10}^6$.

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

On entry, $\mathbf{a}=〈\mathit{\text{value}}〉$ and $\mathbf{b}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{b}\le {10}^6$.

$\mathbf{ifail}=3$

The solution has failed to converge. However, the result should be a reasonable approximation. Requested accuracy not achieved when calculating beta probability. You should try setting tol larger.

$\mathbf{ifail}=4$

The requested accuracy has not been achieved. Use a larger value of tol. There is doubt concerning the accuracy of the computed result. $100$ iterations of the Newton–Raphson method have been performed without satisfying the accuracy criterion (see Section 9). The result should be a reasonable approximation of the solution.

$\mathbf{ifail}=-99$

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 (g01fefe.f90)

10.2

Program Data

Program Data (g01fefe.d)

10.3

Program Results

Program Results (g01fefe.r)