nag_rand_int_hypergeom (g05te) generates a vector of pseudorandom integers from the discrete hypergeometric distribution of the number of specified items in a sample of size

l

, taken from a population of size

k

with

m

specified items in it.

Syntax

[r, state, x, ifail] = g05te(mode, n, ns, np, m, r, state)

[r, state, x, ifail] = nag_rand_int_hypergeom(mode, n, ns, np, m, r, state)

Description

nag_rand_int_hypergeom (g05te) generates

n

integers

x_{i}

from a discrete hypergeometric distribution, where the probability of

x_{i} = I

\begin{matrix} P (i = I) = \frac{l! m! (k - l)! (k - m)!}{I! (l - I)! (m - I)! (k - m - l + I)! k!} & if I = \max (0, m + l - k), \dots, \min (l, m), \\ P (i = I) = 0 & otherwise. \end{matrix}

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_hypergeom (g05te) with the same parameter values can then use this reference vector to generate further variates. The reference array is generated by a recurrence relation if

l m (k - l) (k - m) < 50 k^{3}

, otherwise Stirling's approximation 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_hypergeom (g05te).

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_hypergeom (g05te).
$mode = 2$: 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: $ns$ – int64int32nag_int scalar

l

, the sample size of the hypergeometric distribution.

Constraint:

0 \leq ns \leq np

4: $np$ – int64int32nag_int scalar

k

, the population size of the hypergeometric distribution.

Constraint:

np \geq 0

5: $m$ – int64int32nag_int scalar

m

, the number of specified items of the hypergeometric distribution.

Constraint:

0 \leq m \leq np

6: $r (lr)$ – double array

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

if $mode = 0$ or $2$ , lr must not be too small, but the limit is too complicated to specify;
if $mode = 1$ , lr must remain unchanged from the previous call to nag_rand_int_hypergeom (g05te).

mode = 1

, the reference vector from the previous call to nag_rand_int_hypergeom (g05te).

mode = 3

, r is not referenced.

7: $state (:)$ – 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 pseudorandom numbers from the specified hypergeometric 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: $0 \leq ns \leq np$ .

$ifail = 4$: Constraint: $np \geq 0$ .

$ifail = 5$: Constraint: $0 \leq m \leq np$ .

$ifail = 6$: On entry, some of the elements of the array r have been corrupted or have not been initialized.

The value of ns, np or m is not the same as when r was set up in a previous call with $mode = 0$ or $2$ .

$ifail = 7$: On entry, lr is too small when $mode = 0$ or $2$ .

$ifail = 8$: 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

The example program prints

20

pseudorandom integers from a hypergeometric distribution with

l = 500

m = 900

and

n = 1000

, generated by a single call to nag_rand_int_hypergeom (g05te), after initialization by nag_rand_init_repeat (g05kf).

Open in the MATLAB editor: g05te_example

function g05te_example


fprintf('g05te 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
ns = int64(500);
np = int64(1000);
m = int64(900);

% Generate variates from hypergeomtric distribution
mode = int64(2);
r = zeros(200, 1);
[r, state, x, ifail] = g05te( ...
                              mode, n, ns, np, m, r, state);

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

g05te example results

Variates
   452
   444
   453
   454
   444
   450
   449
   454
   450
   452
   442
   447
   451
   442
   451
   447
   447
   462
   456
   450

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

Chapter Contents

Chapter Introduction

NAG Toolbox