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.

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 ) );
}