@stdlib/stats-base-dists-t-cdf
v0.2.3TypeScript
Student's t distribution cumulative distribution function (CDF).
stdlibstdmathstatisticsstatsdistributiondistprobabilitycdfcumulative distributiondistribution function
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Cumulative Distribution Function
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> [Student's t][t-distribution] distribution [cumulative distribution function][cdf] (CDF).
The [cumulative distribution function][cdf] (CDF) for a [t distribution][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][beta-function].
Installation
``bash`
npm install @stdlib/stats-base-dists-t-cdf
Usage
`javascript`
var cdf = require( '@stdlib/stats-base-dists-t-cdf' );
#### cdf( x, v )
Evaluates the [cumulative distribution function][cdf] (CDF) for a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
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.
`javascript
var y = cdf( NaN, 1.0 );
// returns NaN
y = cdf( 0.0, NaN );
// returns NaN
`
If provided v <= 0, the function returns NaN.
`javascript
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][cdf] of a [Student's t][t-distribution] distribution with degrees of freedom v.
`javascript
var mycdf = cdf.factory( 0.5 );
var y = mycdf( 3.0 );
// returns ~0.816
y = mycdf( 1.0 );
// returns ~0.699
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var cdf = require( '@stdlib/stats-base-dists-t-cdf' );
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, cdf );
`
*
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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[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-t-cdf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-t-cdf/blob/deno/README.md
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[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-t-cdf/main/LICENSE
[beta-function]: https://en.wikipedia.org/wiki/Beta_function
[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function
[t-distribution]: https://en.wikipedia.org/wiki/Student%27s_t-distribution