@stdlib/stats-base-dists-t-logpdf
v0.3.1TypeScript
Natural logarithm of the probability density function (PDF) for a Student's t distribution.
0/weekUpdated yesterdayApache-2.0Unpacked: 53.9 KB
Published by The Stdlib Authors
npm install @stdlib/stats-base-dists-t-logpdfWe believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js. The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases. When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there. To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
About stdlib...
Logarithm of Probability Density Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> Evaluate the natural logarithm of the probability density function (PDF) for a [Student's t][t-distribution] distribution.
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-logpdf
Usage
`javascript`
var logpdf = require( '@stdlib/stats-base-dists-t-logpdf' );
#### logpdf( x, v )
Evaluates the natural logarithm of the [probability density function][pdf] (PDF) for a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
var y = logpdf( 0.3, 4.0 );
// returns ~-1.036
y = logpdf( 2.0, 0.7 );
// returns ~-2.841
y = logpdf( -1.0, 0.5 );
// returns ~-2.134
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = logpdf( NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN );
// returns NaN
`
If provided v <= 0, the function returns NaN.
`javascript
var y = logpdf( 2.0, -1.0 );
// returns NaN
y = logpdf( 2.0, 0.0 );
// returns NaN
`
#### logpdf.factory( v )
Returns a function for evaluating the natural logarithm of the [PDF][pdf] of a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
var mylogpdf = logpdf.factory( 1.0 );
var y = mylogpdf( 3.0 );
// returns ~-3.447
y = mylogpdf( 1.0 );
// returns ~-1.838
`
Notes
- In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var logpdf = require( '@stdlib/stats-base-dists-t-logpdf' );
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, ln(f(x;v)): %0.4f', x, v, logpdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/t/logpdf.h"
#### stdlib_base_dists_t_logpdf( x, v )
Evaluates the natural logarithm of 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_logpdf( 0.5, 1.0 );
// returns ~-1.368
The function accepts the following arguments:
- x: [in] double input value.[in] double
- v: degrees of freedom.
`c`
double stdlib_base_dists_t_logpdf( const double x, const double v );
$3
`c
#include "stdlib/stats/base/dists/t/logpdf.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( 1.0, 100.0 );
y = stdlib_base_dists_t_logpdf( x, v );
printf( "x: %lf, v: %lf, ln(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].
[npm-image]: http://img.shields.io/npm/v/@stdlib/stats-base-dists-t-logpdf.svg
[npm-url]: https://npmjs.org/package/@stdlib/stats-base-dists-t-logpdf
[test-image]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/actions/workflows/test.yml/badge.svg?branch=v0.3.1
[test-url]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/actions/workflows/test.yml?query=branch:v0.3.1
[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/stats-base-dists-t-logpdf/main.svg
[coverage-url]: https://codecov.io/github/stdlib-js/stats-base-dists-t-logpdf?branch=main
[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg
[chat-url]: https://stdlib.zulipchat.com
[stdlib]: https://github.com/stdlib-js/stdlib
[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors
[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-t-logpdf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-t-logpdf/main/LICENSE
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution