Cumulative Distribution Function

Student's t distribution cumulative distribution function (CDF).

The cumulative distribution function (CDF) for a t distribution random variable is

where v > 0 is the degrees of freedom. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the beta function.

Installation

npm install @stdlib/stats-base-dists-t-cdf

Usage

var cdf = require( '@stdlib/stats-base-dists-t-cdf' );

cdf( x, v )

Evaluates the cumulative distribution function (CDF) for a Student's t distribution with degrees of freedom v.

var y = cdf( 2.0, 0.1 );
// returns ~0.611

y = cdf( 1.0, 2.0 );
// returns ~0.789

y = cdf( -1.0, 4.0 );
// returns ~0.187

If provided NaN as any argument, the function returns NaN.

var y = cdf( NaN, 1.0 );
// returns NaN

y = cdf( 0.0, NaN );
// returns NaN

If provided v <= 0, the function returns NaN.

var y = cdf( 2.0, -1.0 );
// returns NaN

y = cdf( 2.0, 0.0 );
// returns NaN

cdf.factory( v )

Returns a function for evaluating the cdf of a Student's t distribution with degrees of freedom v.

var mycdf = cdf.factory( 0.5 );
var y = mycdf( 3.0 );
// returns ~0.816

y = mycdf( 1.0 );
// returns ~0.699

Examples

var randu = require( '@stdlib/random-base-randu' );
var cdf = require( '@stdlib/stats-base-dists-t-cdf' );

var v;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = (randu() * 6.0) - 3.0;
    v = randu() * 10.0;
    y = cdf( x, v );
    console.log( 'x: %d, v: %d, F(x;v): %d', x.toFixed( 4 ), v.toFixed( 4 ), y.toFixed( 4 ) );
}

Notice

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.

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License

See LICENSE.

Copyright

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