Probability Density Function

Student's t distribution probability density function (PDF).

The probability density function (PDF) for a t distribution random variable is

where v > 0 is the degrees of freedom.

Installation

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

Usage

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

pdf( x, v )

Evaluates the probability density function (PDF) for a Student's t distribution with degrees of freedom v.

var y = pdf( 0.3, 4.0 );
// returns ~0.355

y = pdf( 2.0, 0.7 );
// returns ~0.058

y = pdf( -1.0, 0.5 );
// returns ~0.118

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

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

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

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

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

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

pdf.factory( v )

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

var mypdf = pdf.factory( 1.0 );
var y = mypdf( 3.0 );
// returns ~0.032

y = mypdf( 1.0 );
// returns ~0.159

Examples

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var pdf = require( '@stdlib/stats-base-dists-t-pdf' );

var opts = {
    'dtype': 'float64'
};
var x = uniform( 10, -3.0, 3.0, opts );
var v = uniform( 10, 0.0, 10.0, opts );

logEachMap( 'x: %0.4f, v: %0.4f, f(x;v): %0.4f', x, v, pdf );

C APIs

Usage

#include "stdlib/stats/base/dists/t/pdf.h"

stdlib_base_dists_t_pdf( x, v )

Evaluates the probability density function (PDF) for a Student's t distribution with degrees of freedom v.

double out = stdlib_base_dists_t_pdf( 0.3, 4.0 );
// returns ~0.355

The function accepts the following arguments:

• x: [in] double input value.
• v: [in] double degree of freedom.

double stdlib_base_dists_t_pdf( const double x, const double v );

Examples

#include "stdlib/stats/base/dists/t/pdf.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double x;
    double v;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        x = random_uniform( -10.0, 10.0 );
        v = random_uniform( 0.1, 10.0 );
        y = stdlib_base_dists_t_pdf( x, v );
        printf( "x: %lf, v: %lf, f(x;v): %lf\n", x, v, y );
    }
}

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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2026. The Stdlib Authors.