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NAG Toolbox: nag_rand_int_binomial (g05ta)

Purpose

nag_rand_int_binomial (g05ta) generates a vector of pseudorandom integers from the discrete binomial distribution with parameters mm and pp.

Syntax

[r, state, x, ifail] = g05ta(mode, n, m, p, r, state)
[r, state, x, ifail] = nag_rand_int_binomial(mode, n, m, p, r, state)

Description

nag_rand_int_binomial (g05ta) generates nn integers xixi from a discrete binomial distribution, where the probability of xi = Ixi=I is
P(xi = I) = (m ! )/(I ! (mI) ! ) pI × (1p)mI,  I = 0,1,,m,
P(xi=I)= m! I!(m-I)! pI×(1-p)m-I,  I=0,1,,m,
where m0m0 and 0p10p1. This represents the probability of achieving II successes in mm trials when the probability of success at a single trial is pp.
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_binomial (g05ta) with the same parameter values 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_binomial (g05ta).

References

Kendall M G and Stuart A (1969) The Advanced Theory of Statistics (Volume 1) (3rd Edition) Griffin
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 = 0mode=0
Set up reference vector only.
mode = 1mode=1
Generate variates using reference vector set up in a prior call to nag_rand_int_binomial (g05ta).
mode = 2mode=2
Set up reference vector and generate variates.
mode = 3mode=3
Generate variates without using the reference vector.
Constraint: mode = 0mode=0, 11, 22 or 33.
2:     n – int64int32nag_int scalar
nn, the number of pseudorandom numbers to be generated.
Constraint: n0n0.
3:     m – int64int32nag_int scalar
mm, the number of trials of the distribution.
Constraint: m0m0.
4:     p – double scalar
pp, the probability of success of the binomial distribution.
Constraint: 0.0p1.00.0p1.0.
5:     r(lr) – double array
lr, the dimension of the array, must satisfy the constraint
  • if mode = 0mode=0 or 22,
    lr > min (m,int[m × p + 7.15 × sqrt( m × p × (1p) ) + 1])
    max (0,int[m × p7.15 × sqrt( m × p × (1p) )7.15]) + 8
    lr > min(m,int[ m×p+7.15 × m × p × (1-p) +1 ]) - max(0,int[ m × p - 7.15 × m × p × (1-p) - 7.15 ]) +8 ;
  • if mode = 1mode=1, lr must remain unchanged from the previous call to nag_rand_int_binomial (g05ta).
If mode = 1mode=1, the reference vector from the previous call to nag_rand_int_binomial (g05ta).
If mode = 3mode=3, r is not referenced by nag_rand_int_binomial (g05ta).
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.

Input Parameters Omitted from the MATLAB Interface

lr

Output Parameters

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

Error Indicators and Warnings

Errors or warnings detected by the function:
  ifail = 1ifail=1
On entry, mode0mode0, 11, 22 or 33.
  ifail = 2ifail=2
On entry, n < 0n<0.
  ifail = 3ifail=3
On entry, m < 0m<0.
  ifail = 4ifail=4
On entry,p < 0.0p<0.0,
orp > 1.0p>1.0.
  ifail = 5ifail=5
On entry, m or p is not the same as when r was set up in a previous call to nag_rand_int_binomial (g05ta) with mode = 0mode=0 or 22.
On entry, the r vector was not initialized correctly or has been corrupted.
  ifail = 6ifail=6
On entry, lr is too small when mode = 0mode=0 or 22.
  ifail = 7ifail=7
On entry,state vector was not initialized or has been corrupted.

Accuracy

Not applicable.

Further Comments

None.

Example

function nag_rand_int_binomial_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
mode = int64(2);
n = int64(20);
m = int64(6000);
p = 0.8;
r = zeros(6007, 1);
% Initialize the generator to a repeatable sequence
[state, ifail] = nag_rand_init_repeat(genid, subid, seed);
[r, state, x, ifail] = nag_rand_int_binomial(mode, n, m, p, r, state);
 x, ifail
 

x =

                 4811
                 4761
                 4821
                 4826
                 4761
                 4800
                 4791
                 4825
                 4800
                 4814
                 4749
                 4780
                 4810
                 4750
                 4807
                 4782
                 4778
                 4877
                 4840
                 4802


ifail =

                    0


function g05ta_example
% Initialize the seed
seed = [int64(1762543)];
% genid and subid identify the base generator
genid = int64(1);
subid =  int64(1);
mode = int64(2);
n = int64(20);
m = int64(6000);
p = 0.8;
r = zeros(6007, 1);
% Initialize the generator to a repeatable sequence
[state, ifail] = g05kf(genid, subid, seed);
[r, state, x, ifail] = g05ta(mode, n, m, p, r, state);
 x, ifail
 

x =

                 4811
                 4761
                 4821
                 4826
                 4761
                 4800
                 4791
                 4825
                 4800
                 4814
                 4749
                 4780
                 4810
                 4750
                 4807
                 4782
                 4778
                 4877
                 4840
                 4802


ifail =

                    0



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