NAG Library Routine Document

G05THF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     MODE – INTEGERInput

On entry: a code for selecting the operation to be performed by the routine.

$\mathbf{MODE}=0$

Set up reference vector only.

$\mathbf{MODE}=1$

Generate variates using reference vector set up in a prior call to G05THF.

$\mathbf{MODE}=2$

Set up reference vector and generate variates.

$\mathbf{MODE}=3$

Generate variates without using the reference vector.

Constraint: $\mathbf{MODE}=0$, $1$, $2$ or $3$.

2:     N – INTEGERInput

On entry: $n$, the number of pseudorandom numbers to be generated.

Constraint: $\mathbf{N}\ge 0$.

3:     M – INTEGERInput

On entry: $m$, the number of failures of the distribution.

Constraint: $\mathbf{M}\ge 0$.

4:     P – REAL (KIND=nag_wp)Input

On entry: $p$, the parameter of the negative binomial distribution representing the probability of success at a single trial.

Constraint: $0.0\le \mathbf{P}<1.0$.

5:     R(LR) – REAL (KIND=nag_wp) arrayCommunication Array

On entry: if $\mathbf{MODE}=1$, the reference vector from the previous call to G05THF.

If $\mathbf{MODE}=3$, R is not referenced by G05THF.

On exit: the reference vector.

6:     LR – INTEGERInput

On entry: the dimension of the array R as declared in the (sub)program from which G05THF is called.

Suggested values:

• if $\mathbf{MODE}\ne 3$,
  $\mathbf{LR}=28+\left(20\times \sqrt{\mathbf{M}\times \mathbf{P}}+30\times \mathbf{P}\right)/\left(1-\mathbf{P}\right)\text{ approximately}$;
• otherwise $\mathbf{LR}=1$.

Constraints:

• if $\mathbf{MODE}=0$ or $2$,
  $\begin{array}{cc}\mathbf{LR}>& \mathrm{int}\left(\begin{array}{c}\frac{\mathbf{M}\times \mathbf{P}+7.15\times \sqrt{\mathbf{M}\times \mathbf{P}}+20.15\times \mathbf{P}}{1-\mathbf{P}}+8.5\end{array}\right)\\ \\ & -\max \left(\begin{array}{c}0,\mathrm{int}\left(\begin{array}{c}\frac{\mathbf{M}\times \mathbf{P}-7.15\times \sqrt{\mathbf{M}\times \mathbf{P}}}{1-\mathbf{P}}\end{array}\right)\end{array}\right)+9\\ \end{array}$;
• if $\mathbf{MODE}=1$, LR must remain unchanged from the previous call to G05THF.

7:     STATE($*$) – INTEGER arrayCommunication Array

Note: the actual argument supplied must be the array STATE supplied to the initialization routines G05KFF or G05KGF.

On entry: contains information on the selected base generator and its current state.

On exit: contains updated information on the state of the generator.

8:     X(N) – INTEGER arrayOutput

On exit: the $n$ pseudorandom numbers from the specified negative binomial distribution.

9:     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, $\mathbf{MODE}\ne 0$, $1$, $2$ or $3$.

$\mathbf{IFAIL}=2$

On entry, $\mathbf{N}<0$.

$\mathbf{IFAIL}=3$

On entry, $\mathbf{M}<0$.

$\mathbf{IFAIL}=4$

On entry,	$\mathbf{P}<0.0$,
or	$\mathbf{P}\ge 1.0$.

$\mathbf{IFAIL}=5$

On entry, P or M is not the same as when R was set up in a previous call to G05THF with $\mathbf{MODE}=0$ or $2$.

On entry, the R vector was not initialized correctly, or has been corrupted.

$\mathbf{IFAIL}=6$

On entry, LR is too small when $\mathbf{MODE}=0$ or $2$.

$\mathbf{IFAIL}=7$

On entry,

STATE vector was not initialized or has been corrupted.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g05thfe.f90)

9.2  Program Data

Program Data (g05thfe.d)

9.3  Program Results

Program Results (g05thfe.r)