The variates can be generated with or without using a search table and index. If a search table is used then it is stored with the index in a reference vector and subsequent calls to nag_rand_int_negbin (g05th) with the same parameter value can then use this reference vector to generate further variates.

One of the initialization functions nag_rand_init_repeat (g05kf) (for a repeatable sequence if computed sequentially) or nag_rand_init_nonrepeat (g05kg) (for a non-repeatable sequence) must be called prior to the first call to nag_rand_int_negbin (g05th).

References

Knuth D E (1981) The Art of Computer Programming (Volume 2) (2nd Edition) Addison–Wesley

Parameters

Compulsory Input Parameters

1: $mode$ – int64int32nag_int scalar

A code for selecting the operation to be performed by the function.

$mode = 0$: Set up reference vector only.
$mode = 1$: Generate variates using reference vector set up in a prior call to nag_rand_int_negbin (g05th).
$mode = 2$: Set up reference vector and generate variates.
$mode = 3$: Generate variates without using the reference vector.

Constraint:

mode = 0

1

2

3

2: $n$ – int64int32nag_int scalar

n

, the number of pseudorandom numbers to be generated.

Constraint:

n \geq 0

3: $m$ – int64int32nag_int scalar

m

, the number of failures of the distribution.

Constraint:

m \geq 0

4: $p$ – double scalar

p

, the parameter of the negative binomial distribution representing the probability of success at a single trial.

Constraint:

0.0 \leq p < 1.0

5: $r (lr)$ – double array

lr, the dimension of the array, must satisfy the constraint

if $mode = 0$ or $2$ ,
$\begin{matrix} lr > & int (\begin{matrix} \frac{m \times p + 7.15 \times \sqrt{m \times p} + 20.15 \times p}{1 - p} + 8.5 \end{matrix}) \\ - \max (\begin{matrix} 0, int (\begin{matrix} \frac{m \times p - 7.15 \times \sqrt{m \times p}}{1 - p} \end{matrix}) \end{matrix}) + 9 \end{matrix}$ ;
if $mode = 1$ , lr must remain unchanged from the previous call to nag_rand_int_negbin (g05th).

mode = 1

, the reference vector from the previous call to nag_rand_int_negbin (g05th).

mode = 3

, r is not referenced.

6: $state (:)$ – int64int32nag_int array

Note: the actual argument supplied must be the array state supplied to the initialization routines nag_rand_init_repeat (g05kf) or nag_rand_init_nonrepeat (g05kg).

Contains information on the selected base generator and its current state.

Optional Input Parameters

None.

Output Parameters

1: $r (lr)$ – double array: If $mode \neq 3$ , the reference vector.
2: $state (:)$ – int64int32nag_int array: Contains updated information on the state of the generator.
3: $x (n)$ – int64int32nag_int array: The $n$ pseudorandom numbers from the specified negative binomial distribution.
4: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Errors or warnings detected by the function:

$ifail = 1$: Constraint: $mode = 0$ , $1$ , $2$ or $3$ .

$ifail = 2$: Constraint: $n \geq 0$ .

$ifail = 3$: Constraint: $m \geq 0$ .

$ifail = 4$: Constraint: $0.0 \leq p < 1.0$ .

$ifail = 5$: On entry, some of the elements of the array r have been corrupted or have not been initialized.

p or m is not the same as when r was set up in a previous call.

$ifail = 6$: On entry, lr is too small when $mode = 0$ or $2$ .

$ifail = 7$: On entry, state vector has been corrupted or not initialized.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

Not applicable.

Further Comments

None.

Example

This example prints

20

pseudorandom integers from a negative binomial distribution with parameters

m = 60

and

p = 0.999

, generated by a single call to nag_rand_int_negbin (g05th), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05th_example

function g05th_example


fprintf('g05th example results\n\n');

% Initialize the base generator to a repeatable sequence
seed  = [int64(1762543)];
genid = int64(1);
subid = int64(1);
[state, ifail] = g05kf( ...
                        genid, subid, seed);

% Number of variates
n = int64(20);

% Parameters
m = int64(60);
p = 0.999;

% Generate variates from a negative binomial distribution 
% without reference vector
mode = int64(3);
r    = [0];
[r, state, x, ifail] = g05th( ...
                              mode, n, m, p, r, state);

disp('Variates');
disp(double(x));

g05th example results

Variates
       62339
       50505
       64863
       66289
       50434
       59461
       57365
       65965
       59572
       63104
       47833
       54735
       62075
       48018
       61458
       55190
       54263
       80995
       70129
       60200

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox