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Cauchy Random Numbers

Cauchy distributed pseudorandom numbers.

Installation

npm install @stdlib/random-base-cauchy

Alternatively,

To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
If you are using Deno, visit the deno branch (see README for usage intructions).
For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

cauchy( x0, gamma )

Returns a pseudorandom number drawn from a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

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

If x0 or gamma is NaN or gamma <= 0, the function returns NaN.

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

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

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

cauchy.factory( [x0, gamma, ][options] )

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

var rand = cauchy.factory();

var r = rand( 0.0, 1.5 );
// returns <number>

If provided x0 and gamma, the returned generator returns random variates from the specified distribution.

// Draw from Cauchy( 0.0, 1.5 ) distribution:
var rand = cauchy.factory( 0.0, 1.5 );

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

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

If not provided x0 and gamma, the returned generator requires that both parameters be provided at each invocation.

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

var r = rand( 2.0, 3.0 );
// returns <number>

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

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

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

var rand2 = cauchy.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 = cauchy( 2.0, 3.0 );
}

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

// Test that the generated pseudorandom numbers are the same:
bool = ( rand( 2.0, 3.0 ) === cauchy( 2.0, 3.0 ) );
// returns true

cauchy.NAME

The generator name.

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

cauchy.PRNG

The underlying pseudorandom number generator.

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