NAG Library Routine Document

G01SFF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     LTAIL – INTEGERInput

On entry: the length of the array TAIL.

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

2:     TAIL(LTAIL) – CHARACTER(1) arrayInput

On entry: indicates whether a lower or upper tail probability is required. For $j=\left(\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{LTAIL}\right)+1$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{LTAIL},\mathbf{LG},\mathbf{LA},\mathbf{LB}\right)$:

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

The lower tail probability is returned, i.e., $p_i=P\left(G_i\le g_i:{\alpha }_i,{\beta }_i\right)$.

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

The upper tail probability is returned, i.e., $p_i=P\left(G_i\ge g_i:{\alpha }_i,{\beta }_i\right)$.

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

3:     LG – INTEGERInput

On entry: the length of the array G.

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

4:     G(LG) – REAL (KIND=nag_wp) arrayInput

On entry: $g_i$, the value of the gamma variate with $g_i=\mathbf{G}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LG}\right)+1$.

Constraint: $\mathbf{G}\left(\mathit{j}\right)\ge 0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LG}$.

5:     LA – INTEGERInput

On entry: the length of the array A.

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

6:     A(LA) – REAL (KIND=nag_wp) arrayInput

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

Constraint: $\mathbf{A}\left(\mathit{j}\right)>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LA}$.

7:     LB – INTEGERInput

On entry: the length of the array B.

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

8:     B(LB) – REAL (KIND=nag_wp) arrayInput

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

Constraint: $\mathbf{B}\left(\mathit{j}\right)>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LB}$.

9:     P($*$) – REAL (KIND=nag_wp) arrayOutput

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

On exit: $p_i$, the probabilities of the beta distribution.

10:   IVALID($*$) – INTEGER arrayOutput

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

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 $p_i$.

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

On entry,

$g_i<0.0$.

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

On entry,	${\alpha }_i\le 0.0$,
or	${\beta }_i\le 0.0$.

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

The solution did not converge in $600$ iterations, see S14BAF for details. The probability returned should be a reasonable approximation to the solution.

11:   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, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ 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, at least one value of G, A, B or TAIL was invalid, or the solution did not 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: $\mathbf{LG}>0$.

$\mathbf{IFAIL}=4$

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

$\mathbf{IFAIL}=5$

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

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01sffe.f90)

9.2  Program Data

Program Data (g01sffe.d)

9.3  Program Results

Program Results (g01sffe.r)