time-to-botec/squiggle/node_modules/@stdlib/random/base/beta/README.md

Beta Random Numbers

Beta distributed pseudorandom numbers.

Usage

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

beta( alpha, beta )

Returns a pseudorandom number drawn from a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var r = beta( 2.0, 5.0 );
// returns <number>

If alpha <= 0 or beta <= 0, the function returns NaN.

var r = beta( 2.0, -2.0 );
// returns NaN

r = beta( -2.0, 2.0 );
// returns NaN

If alpha or beta is NaN, the function returns NaN.

var r = beta( NaN, 5.0 );
// returns NaN

r = beta( 2.0, NaN );
// returns NaN

beta.factory( [alpha, beta, ][options] )

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

var rand = beta.factory();

var r = rand( 1.5, 1.5 );
// returns <number>

If provided alpha and beta, the returned generator returns random variates from the specified distribution.

// Draw from beta( 1.5, 1.5 ) distribution:
var rand = beta.factory( 1.5, 1.5 );

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

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

If not provided alpha and beta, the returned generator requires that both parameters be provided at each invocation.

var rand = beta.factory();

var r = rand( 1.0, 1.0 );
// returns <number>

r = rand( 3.14, 2.25 );
// returns <number>

The function accepts the following options:

• prng: pseudorandom number generator for generating uniformly distributed pseudorandom numbers on the interval [0,1). If provided, the function ignores both the state and seed options. In order to seed the returned pseudorandom number generator, one must seed the provided prng (assuming the provided prng is seedable).
• seed: pseudorandom number generator seed.
• state: a Uint32Array containing pseudorandom number generator state. If provided, the function ignores the seed option.
• copy: boolean indicating whether to copy a provided pseudorandom number generator state. Setting this option to false allows sharing state between two or more pseudorandom number generators. Setting this option to true ensures that a returned generator has exclusive control over its internal state. Default: true.

To use a custom PRNG as the underlying source of uniformly distributed pseudorandom numbers, set the prng option.

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

var rand = beta.factory({
    'prng': minstd.normalized
});

var r = rand( 2.0, 4.0 );
// returns <number>

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

var rand1 = beta.factory({
    'seed': 12345
});

var r1 = rand1( 2.0, 3.0 );
// returns <number>

var rand2 = beta.factory( 2.0, 3.0, {
    'seed': 12345
});

var r2 = rand2();
// returns <number>

var bool = ( r1 === r2 );
// returns true

To return a generator having a specific initial state, set the generator state option.

var rand;
var bool;
var r;
var i;

// Generate pseudorandom numbers, thus progressing the generator state:
for ( i = 0; i < 1000; i++ ) {
    r = beta( 2.0, 4.0 );
}

// Create a new PRNG initialized to the current state of `beta`:
rand = beta.factory({
    'state': beta.state
});

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 2.0, 4.0 ) === beta( 2.0, 4.0 ) );
// returns true

beta.NAME

The generator name.

var str = beta.NAME;
// returns 'beta'

beta.PRNG

The underlying pseudorandom number generator.

var prng = beta.PRNG;
// returns <Function>

beta.seed

The value used to seed beta().

var rand;
var r;
var i;

// Generate pseudorandom values...
for ( i = 0; i < 100; i++ ) {
    r = beta( 2.0, 2.0 );
}

// Generate the same pseudorandom values...
rand = beta.factory( 2.0, 2.0, {
    'seed': beta.seed
});
for ( i = 0; i < 100; i++ ) {
    r = rand();
}

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = beta.factory({
    'prng': Math.random
});

var seed = rand.seed;
// returns null

beta.seedLength

Length of generator seed.

var len = beta.seedLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = beta.factory({
    'prng': Math.random
});

var len = rand.seedLength;
// returns null

beta.state

Writable property for getting and setting the generator state.

var r = beta( 2.0, 5.0 );
// returns <number>

r = beta( 2.0, 5.0 );
// returns <number>

// ...

// Get a copy of the current state:
var state = beta.state;
// returns <Uint32Array>

r = beta( 2.0, 5.0 );
// returns <number>

r = beta( 2.0, 5.0 );
// returns <number>

// Reset the state:
beta.state = state;

// Replay the last two pseudorandom numbers:
r = beta( 2.0, 5.0 );
// returns <number>

r = beta( 2.0, 5.0 );
// returns <number>

// ...

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = beta.factory({
    'prng': Math.random
});

var state = rand.state;
// returns null

beta.stateLength

Length of generator state.

var len = beta.stateLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = beta.factory({
    'prng': Math.random
});

var len = rand.stateLength;
// returns null

beta.byteLength

Size (in bytes) of generator state.

var sz = beta.byteLength;
// returns <number>

If provided a PRNG for uniformly distributed numbers, this value is null.

var rand = beta.factory({
    'prng': Math.random
});

var sz = rand.byteLength;
// returns null

beta.toJSON()

Serializes the pseudorandom number generator as a JSON object.

var o = beta.toJSON();
// returns { 'type': 'PRNG', 'name': '...', 'state': {...}, 'params': [] }

If provided a PRNG for uniformly distributed numbers, this method returns null.

var rand = beta.factory({
    'prng': Math.random
});

var o = rand.toJSON();
// returns null

Notes

• If PRNG state is "shared" (meaning a state array was provided during PRNG creation and not copied) and one sets the generator state to a state array having a different length, the PRNG does not update the existing shared state and, instead, points to the newly provided state array. In order to synchronize PRNG output according to the new shared state array, the state array for each relevant PRNG must be explicitly set.
• If PRNG state is "shared" and one sets the generator state to a state array of the same length, the PRNG state is updated (along with the state of all other PRNGs sharing the PRNG's state array).

Examples

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

var seed;
var rand;
var i;

// Generate pseudorandom numbers...
for ( i = 0; i < 100; i++ ) {
    console.log( beta( 2.0, 2.0 ) );
}

// Create a new pseudorandom number generator...
seed = 1234;
rand = beta.factory( 6.0, 2.0, {
    'seed': seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

// Create another pseudorandom number generator using a previous seed...
rand = beta.factory( 2.0, 2.0, {
    'seed': beta.seed
});
for ( i = 0; i < 100; i++ ) {
    console.log( rand() );
}

---

References

• Ahrens, J.H., and U. Dieter. 1974. "Computer methods for sampling from gamma, beta, poisson and bionomial distributions." Computing 12 (3): 223–46. doi:10.1007/BF02293108.
• Jöhnk, M.D. 1964. "Erzeugung von Betaverteilten Und Gammaverteilten Zufallszahlen." Metrika 8: 5–15. <http://eudml.org/doc/175224>.