@stdlib/stats-base-dists-t-pdf
v0.3.1TypeScript
Student's t distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [Student's t][t-distribution] distribution probability density function (PDF).
The [probability density function][pdf] (PDF) for a [t distribution][t-distribution] random variable is
where v > 0 is the degrees of freedom.
Installation
``bash`
npm install @stdlib/stats-base-dists-t-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-t-pdf' );
#### pdf( x, v )
Evaluates the [probability density function][pdf] (PDF) for a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
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.
`javascript
var y = pdf( NaN, 1.0 );
// returns NaN
y = pdf( 0.0, NaN );
// returns NaN
`
If provided v <= 0, the function returns NaN.
`javascript
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][pdf] of a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
var mypdf = pdf.factory( 1.0 );
var y = mypdf( 3.0 );
// returns ~0.032
y = mypdf( 1.0 );
// returns ~0.159
`
Examples
`javascript
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
$3
`c`
#include "stdlib/stats/base/dists/t/pdf.h"
#### stdlib_base_dists_t_pdf( x, v )
Evaluates the [probability density function][pdf] (PDF) for a [Student's t][t-distribution] distribution with degrees of freedom v.
`c`
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.[in] double
- v: degree of freedom.
`c`
double stdlib_base_dists_t_pdf( const double x, const double v );
$3
`c
#include "stdlib/stats/base/dists/t/pdf.h"
#include
#include
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][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution