# Binomial Random Numbers

Binomial distributed pseudorandom numbers.

## Usage

``````var binomial = require( '@stdlib/random/base/binomial' );
``````

#### binomial( n, p )

Returns a pseudorandom number drawn from a binomial distribution with number of trials `n` and success probability `p`.

``````var r = binomial( 20, 0.8 );
// returns <number>
``````

If `n` is not a positive integer or `p` is not a probability, the function returns `NaN`.

``````var r = binomial( 1.5, 0.5 );
// returns NaN

r = binomial( 2, 1.5 );
// returns NaN
``````

If `n` or `p` is `NaN`, the function returns `NaN`.

``````var r = binomial( NaN, 0.4 );
// returns NaN

r = binomial( 20, NaN );
// returns NaN
``````

#### binomial.factory( [n, p, ][options] )

Returns a pseudorandom number generator (PRNG) for generating pseudorandom numbers drawn from a binomial distribution.

``````var rand = binomial.factory();

var r = rand( 20, 0.3 );
// returns <number>
``````

If provided `n` and `p`, the returned generator returns random variates from the specified distribution.

``````// Draws from binomial( 10, 0.8 ):
var rand = binomial.factory( 10, 0.8 );

var r = rand();
// returns <number>

r = rand();
// returns <number>
``````

If not provided `n` and `p`, the returned generator requires that both parameters be provided at each invocation.

``````var rand = binomial.factory();

var r = rand( 20, 0.8 );
// returns <number>

r = rand( 123, 0.21 );
// returns <number>
``````

The function accepts the following `options`:

• seed: pseudorandom number generator seed.

To seed a pseudorandom number generator, set the `seed` option.

``````var rand = binomial.factory({
'seed': 12345
});

var r = binomial( 8, 0.9 );
// returns <number>

rand = binomial.factory( 100, 0.2, {
'seed': 12345
});

r = rand();
// returns <number>
``````

#### binomial.NAME

The generator name.

``````var str = binomial.NAME;
// returns 'binomial'
``````

#### binomial.PRNG

The underlying pseudorandom number generator.

``````var prng = binomial.PRNG;
// returns <Function>
``````

#### binomial.SEED

The value used to seed `binomial()`.

``````var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
r = binomial( 20, 0.5 );
}

// Generate the same pseudorandom values...
rand = binomial.factory( 20, 0.5, {
'seed': binomial.SEED
});
for ( i = 0; i < 100; i++ ) {
r = rand();
}
``````

## Examples

``````var binomial = require( '@stdlib/random/base/binomial' );

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
console.log( '\nseed: %d', binomial.SEED );
for ( i = 0; i < 100; i++ ) {
console.log( binomial( 0.5 ) );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = binomial.factory( 0.8, {
'seed': seed
});
console.log( '\nseed: %d', seed );
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = binomial.factory( 0.5, {
'seed': binomial.SEED
});
console.log( '\nseed: %d', binomial.SEED );
for ( i = 0; i < 100; i++ ) {
console.log( rand() );
}
``````

## References

• Hörmann, Wolfgang. 1993. "The generation of binomial random variates." Journal of Statistical Computation and Simulation 46 (1-2): 101–10. doi:10.1080/00949659308811496.