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_geom (g05tc) with the same parameter value can then use this reference vector to generate further variates. If the search table is not used (as recommended for small values of

p

) then a direct transformation of uniform variates is used.

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_geom (g05tc).

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_geom (g05tc).
$mode = 2$: 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: $p$ – double scalar

The parameter

p

of the geometric distribution representing the probability of success at a single trial.

Constraint:

machine precision \leq p \leq 1.0

(see nag_machine_precision (x02aj)).

4: $r (lr)$ – double array

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

if $mode = 0$ or $2$ , $lr \geq 30 / p + 8$ ;
if $mode = 1$ , lr should remain unchanged from the previous call to nag_rand_int_geom (g05tc).

mode = 1

, the reference vector from the previous call to nag_rand_int_geom (g05tc).

mode = 3

, r is not referenced.

5: $state (:)$ – 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 geometric 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: $machine precision \leq p \leq 1.0$ .

p is so small that lr would have to be larger than the largest representable integer.

$ifail = 4$: On entry, some of the elements of the array r have been corrupted or have not been initialized.

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

$ifail = 5$: On entry, lr is too small when $mode = 0$ or $2$ .

$ifail = 6$: 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

The time taken to set up the reference vector, if used, increases with the length of array r. However, if the reference vector is used, the time taken to generate numbers decreases as the space allotted to the index part of r increases. Nevertheless, there is a point, depending on the distribution, where this improvement becomes very small and the suggested value for the length of array r is designed to approximate this point.

If p is very small then the storage requirements for the reference vector and the time taken to set up the reference vector becomes prohibitive. In this case it is recommended that the reference vector is not used. This is achieved by selecting

mode = 3

Example

This example prints

10

pseudorandom integers from a geometric distribution with parameter

p = 0.001

, generated by a single call to nag_rand_int_geom (g05tc), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05tc_example

function g05tc_example


fprintf('g05tc 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(10);

% Parameters
p = 0.001;

% Generate variates from a geometric distribution withouut reference vector
mode = int64(3);
r    = [0];
[r, state, x, ifail] = g05tc( ...
                              mode, n, p, r, state);

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

g05tc example results

Variates
         451
        2238
         292
         225
        2256
         708
         955
         239
         696
         397

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

Chapter Contents

Chapter Introduction

NAG Toolbox