Cauchy distribution cumulative distribution function (CDF).
APACHE-2.0 License
Cauchy distribution cumulative distribution function.
The cumulative distribution function for a Cauchy random variable is
F(x; x_0,\gamma)=\frac{1}{\pi} \mathop{\mathrm{arctan}} \left(\frac{x-x_0}{\gamma}\right)+\frac{1}{2}
where x0
is the location parameter and gamma > 0
is the scale parameter.
npm install @stdlib/stats-base-dists-cauchy-cdf
Alternatively,
script
tag without installation and bundlers, use the ES Module available on the esm
branch (see README).deno
branch (see README for usage intructions).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.
var cdf = require( '@stdlib/stats-base-dists-cauchy-cdf' );
Evaluates the cumulative distribution function (CDF) for a Cauchy distribution with parameters x0
(location parameter) and gamma > 0
(scale parameter).
var y = cdf( 4.0, 0.0, 2.0 );
// returns ~0.852
y = cdf( 1.0, 0.0, 2.0 );
// returns ~0.648
y = cdf( 1.0, 3.0, 2.0 );
// returns 0.25
If provided NaN
as any argument, the function returns NaN
.
var y = cdf( NaN, 0.0, 2.0 );
// returns NaN
y = cdf( 1.0, 2.0, NaN );
// returns NaN
y = cdf( 1.0, NaN, 3.0 );
// returns NaN
If provided gamma <= 0
, the function returns NaN
.
var y = cdf( 2.0, 0.0, -1.0 );
// returns NaN
y = cdf( 2.0, 0.0, 0.0 );
// returns NaN
Returns a function for evaluating the cumulative distribution function of a Cauchy distribution with parameters x0
(location parameter) and gamma > 0
(scale parameter).
var mycdf = cdf.factory( 10.0, 2.0 );
var y = mycdf( 10.0 );
// returns 0.5
y = mycdf( 12.0 );
// returns 0.75
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var cdf = require( '@stdlib/stats-base-dists-cauchy-cdf' );
var gamma;
var x0;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
x0 = randu() * 10.0;
gamma = ( randu()*10.0 ) + EPS;
y = cdf( x, x0, gamma );
console.log( 'x: %d, x0: %d, γ: %d, F(x;x0,γ): %d', x.toFixed( 4 ), x0.toFixed( 4 ), gamma.toFixed( 4 ), y.toFixed( 4 ) );
}
This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.
See LICENSE.
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