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NAG Toolbox: nag_rand_int_negbin (g05th)

 Contents

    1  Purpose
    2  Syntax
    7  Accuracy
    9  Example

Purpose

nag_rand_int_negbin (g05th) generates a vector of pseudorandom integers from the discrete negative binomial distribution with parameter m and probability p of success at a trial.

Syntax

[r, state, x, ifail] = g05th(mode, n, m, p, r, state)
[r, state, x, ifail] = nag_rand_int_negbin(mode, n, m, p, r, state)

Description

nag_rand_int_negbin (g05th) generates n integers xi from a discrete negative binomial distribution, where the probability of xi=I (I successes before m failures) is
Pxi=I= m+I-1! I!m-1! ×pI×1-pm,  I=0,1,.  
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 or 3.
2:     n int64int32nag_int scalar
n, the number of pseudorandom numbers to be generated.
Constraint: n0.
3:     m int64int32nag_int scalar
m, the number of failures of the distribution.
Constraint: m0.
4:     p – double scalar
p, the parameter of the negative binomial distribution representing the probability of success at a single trial.
Constraint: 0.0p<1.0.
5:     rlr – double array
lr, the dimension of the array, must satisfy the constraint
  • if mode=0 or 2,
    lr> int m×p+7.15 × m×p+ 20.15×p 1-p +8.5 - max 0,int m× p-7.15 × m×p 1-p +9 ;
  • if mode=1, lr must remain unchanged from the previous call to nag_rand_int_negbin (g05th).
If mode=1, the reference vector from the previous call to nag_rand_int_negbin (g05th).
If 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:     rlr – double array
If mode3, the reference vector.
2:     state: int64int32nag_int array
Contains updated information on the state of the generator.
3:     xn 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: n0.
   ifail=3
Constraint: m0.
   ifail=4
Constraint: 0.0p<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).
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
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