NAG Library Routine Document

G01TEF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{LTAIL}$ – INTEGERInput

On entry: the length of the array TAIL.

Constraint: $\mathbf{LTAIL}>0$.

2:     $\mathrm{TAIL}\left(\mathbf{LTAIL}\right)$ – CHARACTER(1) arrayInput

On entry: indicates which tail the supplied probabilities represent. For $j=\left(\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{LTAIL}\right)+1$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{LTAIL},\mathbf{LP},\mathbf{LA},\mathbf{LB}\right)$:

$\mathbf{TAIL}\left(j\right)=\text{'L'}$

The lower tail probability, i.e., $p_i=P\left(B_i\le {\beta }_{p_i}:a_i,b_i\right)$.

$\mathbf{TAIL}\left(j\right)=\text{'U'}$

The upper tail probability, i.e., $p_i=P\left(B_i\ge {\beta }_{p_i}:a_i,b_i\right)$.

Constraint: $\mathbf{TAIL}\left(\mathit{j}\right)=\text{'L'}$ or $\text{'U'}$, for $\mathit{j}=1,2,\dots ,\mathbf{LTAIL}$.

3:     $\mathrm{LP}$ – INTEGERInput

On entry: the length of the array P.

Constraint: $\mathbf{LP}>0$.

4:     $\mathrm{P}\left(\mathbf{LP}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: $p_i$, the probability of the required beta distribution as defined by TAIL with $p_i=\mathbf{P}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LP}\right)+1$.

Constraint: $0.0\le \mathbf{P}\left(\mathit{j}\right)\le 1.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LP}$.

5:     $\mathrm{LA}$ – INTEGERInput

On entry: the length of the array A.

Constraint: $\mathbf{LA}>0$.

6:     $\mathrm{A}\left(\mathbf{LA}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: $a_i$, the first parameter of the required beta distribution with $a_i=\mathbf{A}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LA}\right)+1$.

Constraint: $0.0<\mathbf{A}\left(\mathit{j}\right)\le {10}^6$, for $\mathit{j}=1,2,\dots ,\mathbf{LA}$.

7:     $\mathrm{LB}$ – INTEGERInput

On entry: the length of the array B.

Constraint: $\mathbf{LB}>0$.

8:     $\mathrm{B}\left(\mathbf{LB}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: $b_i$, the second parameter of the required beta distribution with $b_i=\mathbf{B}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LB}\right)+1$.

Constraint: $0.0<\mathbf{B}\left(\mathit{j}\right)\le {10}^6$, for $\mathit{j}=1,2,\dots ,\mathbf{LB}$.

9:     $\mathrm{TOL}$ – REAL (KIND=nag_wp)Input

On entry: the relative accuracy required by you in the results. If G01TEF is entered with TOL greater than or equal to $1.0$ or less than $10\times \mathit{machine precision}$ (see X02AJF), then the value of $10\times \mathit{machine precision}$ is used instead.

10:   $\mathrm{BETA}\left(*\right)$ – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array BETA must be at least $\max \left(\mathbf{LTAIL},\mathbf{LP},\mathbf{LA},\mathbf{LB}\right)$.

On exit: ${\beta }_{p_i}$, the deviates for the beta distribution.

11:   $\mathrm{IVALID}\left(*\right)$ – INTEGER arrayOutput

Note: the dimension of the array IVALID must be at least $\max \left(\mathbf{LTAIL},\mathbf{LP},\mathbf{LA},\mathbf{LB}\right)$.

On exit: $\mathbf{IVALID}\left(i\right)$ indicates any errors with the input arguments, with

$\mathbf{IVALID}\left(i\right)=0$

No error.

$\mathbf{IVALID}\left(i\right)=1$

On entry,

invalid value supplied in TAIL when calculating ${\beta }_{p_i}$.

$\mathbf{IVALID}\left(i\right)=2$

On entry,	$p_i<0.0$,
or	$p_i>1.0$.

$\mathbf{IVALID}\left(i\right)=3$

On entry,	$a_i\le 0.0$,
or	$a_i>{10}^6$,
or	$b_i\le 0.0$,
or	$b_i>{10}^6$.

$\mathbf{IVALID}\left(i\right)=4$

The solution has not converged but the result should be a reasonable approximation to the solution.

$\mathbf{IVALID}\left(i\right)=5$

Requested accuracy not achieved when calculating the beta probability. The result should be a reasonable approximation to the correct solution.

12:   $\mathrm{IFAIL}$ – 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, at least one value of TAIL, P, A, or B was invalid, or the solution failed to converge.
Check IVALID for more information.

$\mathbf{IFAIL}=2$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LTAIL}>0$.

$\mathbf{IFAIL}=3$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LP}>0$.

$\mathbf{IFAIL}=4$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LA}>0$.

$\mathbf{IFAIL}=5$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LB}>0$.

$\mathbf{IFAIL}=-99$

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

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

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

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01tefe.f90)

10.2  Program Data

Program Data (g01tefe.d)

10.3  Program Results

Program Results (g01tefe.r)