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Student's T

Student's t distribution constructor.

Installation

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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

T( [v] )

Returns a Student's t distribution object.

var t = new T();

var mu = t.mean;
// returns NaN

By default, v = 1.0. To create a distribution having a different degrees of freedom v, provide a parameter value.

var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0

---

t

A Student's t distribution object has the following properties and methods...

Writable Properties

t.v

Degrees of freedom of the distribution. v must be a positive number.

var t = new T( 2.0 );

var v = t.v;
// returns 2.0

t.v = 3.0;

v = t.v;
// returns 3.0

---

Computed Properties

T.prototype.entropy

Returns the differential entropy.

var t = new T( 4.0 );

var entropy = t.entropy;
// returns ~1.682

T.prototype.kurtosis

Returns the excess kurtosis.

var t = new T( 4.0 );

var kurtosis = t.kurtosis;
// returns Infinity

T.prototype.mean

Returns the expected value.

var t = new T( 4.0 );

var mu = t.mean;
// returns 0.0

T.prototype.median

Returns the median.

var t = new T( 4.0 );

var median = t.median;
// returns 0.0

T.prototype.mode

Returns the mode.

var t = new T( 4.0 );

var mode = t.mode;
// returns 0.0

T.prototype.skewness

Returns the skewness.

var t = new T( 4.0 );

var skewness = t.skewness;
// returns 0.0

T.prototype.stdev

Returns the standard deviation.

var t = new T( 4.0 );

var s = t.stdev;
// returns ~1.414

T.prototype.variance

Returns the variance.

var t = new T( 4.0 );

var s2 = t.variance;
// returns 2.0

---

Methods

T.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var t = new T( 2.0 );

var y = t.cdf( 0.5 );
// returns ~0.667

T.prototype.logcdf( x )

Evaluates the natural logarithm of the cumulative distribution function (CDF).

var t = new T( 2.0 );

var y = t.logcdf( 0.5 );
// returns ~-0.405

T.prototype.logpdf( x )

Evaluates the natural logarithm of the probability density function (PDF).

var t = new T( 2.0 );

var y = t.logpdf( 0.8 );
// returns ~-1.456

T.prototype.pdf( x )

Evaluates the probability density function (PDF).

var t = new T( 2.0 );

var y = t.pdf( 0.8 );
// returns ~0.233

T.prototype.quantile( p )

Evaluates the quantile function at probability p.

var t = new T( 2.0 );

var y = t.quantile( 0.5 );
// returns 0.0

y = t.quantile( 1.9 );
// returns NaN

---

Examples

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

var t = new T( 2.0 );

var mu = t.mean;
// returns 0.0

var mode = t.mode;
// returns 0.0

var s2 = t.variance;
// returns Infinity

var y = t.cdf( 0.8 );
// returns ~0.746

---

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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.