Lévy Random Numbers

Usage

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

levy( mu, c )

Returns a pseudorandom number drawn from a Lévy distribution with parameters mu (location parameter) and c (scale parameter).

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

If mu or c is NaN or c <= 0, the function returns NaN.

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

r = levy( NaN, 5.0 );
// returns NaN

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

levy.factory( [mu, c, ][options] )

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

var rand = levy.factory();

var r = rand( 0.1, 1.5 );
// returns <number>

If provided mu and c, the returned generator returns random variates from the specified distribution.

var rand = levy.factory( 10.0, 2.0 );

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

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

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

var rand = levy.factory();

var r = rand( 0.0, 1.0 );
// returns <number>

r = rand( -2.0, 2.0 );
// 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 = levy.factory({
    'prng': minstd.normalized
});

var r = rand( 1.0, 2.0 );
// returns <number>

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

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

var r1 = rand1( 1.0, 2.0 );
// returns <number>

var rand2 = levy.factory( 1.0, 2.0, {
    '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 = levy( 1.0, 2.0 );
}

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

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 1.0, 2.0 ) === levy( 1.0, 2.0 ) );
// returns true

levy.NAME

The generator name.

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

levy.PRNG

The underlying pseudorandom number generator.

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

levy.seed

The value used to seed levy().

var rand;
var r;
var i;

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

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

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

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

var seed = rand.seed;
// returns null

levy.seedLength

Length of generator seed.

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

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

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

var len = rand.seedLength;
// returns null

levy.state

Writable property for getting and setting the generator state.

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

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

// ...

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

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

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

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

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

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

// ...

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

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

var state = rand.state;
// returns null

levy.stateLength

Length of generator state.

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

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

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

var len = rand.stateLength;
// returns null

levy.byteLength

Size (in bytes) of generator state.

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

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

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

var sz = rand.byteLength;
// returns null

levy.toJSON()

Serializes the pseudorandom number generator as a JSON object.

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

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

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

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