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Arcsine

Arcsine distribution constructor.

Installation

npm install @stdlib/stats-base-dists-arcsine-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 Arcsine = require( '@stdlib/stats-base-dists-arcsine-ctor' );

Arcsine( [a, b] )

Returns an arcsine distribution object.

var arcsine = new Arcsine();

var mu = arcsine.mean;
// returns 0.5

By default, a = 0.0 and b = 1.0. To create a distribution having a different a (minimum support) and b (maximum support), provide the corresponding arguments.

var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0

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arcsine

An arcsine distribution object has the following properties and methods...

Writable Properties

arcsine.a

Minimum support of the distribution. a must be a number less than b.

var arcsine = new Arcsine();

var a = arcsine.a;
// returns 0.0

arcsine.a = 0.5;

a = arcsine.a;
// returns 0.5

arcsine.b

Maximum support of the distribution. b must be a number greater than a.

var arcsine = new Arcsine( 2.0, 4.0 );

var b = arcsine.b;
// returns 4.0

arcsine.b = 3.0;

b = arcsine.b;
// returns 3.0

---

Computed Properties

Arcsine.prototype.entropy

Returns the differential entropy.

var arcsine = new Arcsine( 4.0, 12.0 );

var entropy = arcsine.entropy;
// returns ~1.838

Arcsine.prototype.kurtosis

Returns the excess kurtosis.

var arcsine = new Arcsine( 4.0, 12.0 );

var kurtosis = arcsine.kurtosis;
// returns -1.5

Arcsine.prototype.mean

Returns the expected value.

var arcsine = new Arcsine( 4.0, 12.0 );

var mu = arcsine.mean;
// returns 8.0

Arcsine.prototype.median

Returns the median.

var arcsine = new Arcsine( 4.0, 12.0 );

var median = arcsine.median;
// returns 8.0

Arcsine.prototype.mode

Returns the mode.

var arcsine = new Arcsine( 4.0, 12.0 );

var mode = arcsine.mode;
// returns 4.0

Arcsine.prototype.skewness

Returns the skewness.

var arcsine = new Arcsine( 4.0, 12.0 );

var skewness = arcsine.skewness;
// returns 0.0

Arcsine.prototype.stdev

Returns the standard deviation.

var arcsine = new Arcsine( 4.0, 12.0 );

var s = arcsine.stdev;
// returns ~2.828

Arcsine.prototype.variance

Returns the variance.

var arcsine = new Arcsine( 4.0, 12.0 );

var s2 = arcsine.variance;
// returns 8.0

---

Methods

Arcsine.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.cdf( 2.5 );
// returns ~0.333

Arcsine.prototype.logcdf( x )

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

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logcdf( 2.5 );
// returns ~-1.1

Arcsine.prototype.logpdf( x )

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

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.logpdf( 2.5 );
// returns ~-1.0

Arcsine.prototype.pdf( x )

Evaluates the probability density function (PDF).

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.pdf( 2.5 );
// returns ~0.368

Arcsine.prototype.quantile( p )

Evaluates the quantile function at probability p.

var arcsine = new Arcsine( 2.0, 4.0 );

var y = arcsine.quantile( 0.5 );
// returns 3.0

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

---

Examples

var Arcsine = require( '@stdlib/stats-base-dists-arcsine-ctor' );

var arcsine = new Arcsine( 2.0, 4.0 );

var mu = arcsine.mean;
// returns 3.0

var median = arcsine.median;
// returns 3.0

var s2 = arcsine.variance;
// returns 0.5

var y = arcsine.cdf( 2.5 );
// returns ~0.333

---

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.