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Laplace

Laplace distribution constructor.

Installation

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

Laplace( [mu, b] )

Returns a Laplace distribution object.

var laplace = new Laplace();

var mu = laplace.mean;
// returns 0.0

By default, mu = 0.0 and b = 1.0. To create a distribution having a different mu (location parameter) and b (scale parameter), provide the corresponding arguments.

var laplace = new Laplace( 2.0, 4.0 );

var mu = laplace.mean;
// returns 2.0

---

laplace

A Laplace distribution object has the following properties and methods...

Writable Properties

laplace.mu

Location parameter of the distribution.

var laplace = new Laplace();

var mu = laplace.mu;
// returns 0.0

laplace.mu = 3.0;

mu = laplace.mu;
// returns 3.0

laplace.b

Scale parameter of the distribution. b must be a positive number.

var laplace = new Laplace( 2.0, 4.0 );

var b = laplace.b;
// returns 4.0

laplace.b = 3.0;

b = laplace.b;
// returns 3.0

---

Computed Properties

Laplace.prototype.entropy

Returns the differential entropy.

var laplace = new Laplace( 4.0, 12.0 );

var entropy = laplace.entropy;
// returns ~4.178

Laplace.prototype.kurtosis

Returns the excess kurtosis.

var laplace = new Laplace( 4.0, 12.0 );

var kurtosis = laplace.kurtosis;
// returns 3.0

Laplace.prototype.mean

Returns the expected value.

var laplace = new Laplace( 4.0, 12.0 );

var mu = laplace.mean;
// returns 4.0

Laplace.prototype.median

Returns the median.

var laplace = new Laplace( 4.0, 12.0 );

var median = laplace.median;
// returns 4.0

Laplace.prototype.mode

Returns the mode.

var laplace = new Laplace( 4.0, 12.0 );

var mode = laplace.mode;
// returns 4.0

Laplace.prototype.skewness

Returns the skewness.

var laplace = new Laplace( 4.0, 12.0 );

var skewness = laplace.skewness;
// returns 0.0

Laplace.prototype.stdev

Returns the standard deviation.

var laplace = new Laplace( 4.0, 12.0 );

var s = laplace.stdev;
// returns ~16.971

Laplace.prototype.variance

Returns the variance.

var laplace = new Laplace( 4.0, 12.0 );

var s2 = laplace.variance;
// returns 288.0

---

Methods

Laplace.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.cdf( 0.5 );
// returns ~0.344

Laplace.prototype.logcdf( x )

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

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.logcdf( 2.0 );
// returns ~-0.693

Laplace.prototype.logpdf( x )

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

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.logpdf( 0.8 );
// returns ~-2.379

Laplace.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.mgf( 0.2 );
// returns ~4.144

Laplace.prototype.pdf( x )

Evaluates the probability density function (PDF).

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.pdf( 2.0 );
// returns 0.125

Laplace.prototype.quantile( p )

Evaluates the quantile function at probability p.

var laplace = new Laplace( 2.0, 4.0 );

var y = laplace.quantile( 0.5 );
// returns 2.0

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

---

Examples

var Laplace = require( '@stdlib/stats-base-dists-laplace-ctor' );

var laplace = new Laplace( 2.0, 4.0 );

var mean = laplace.mean;
// returns 2.0

var median = laplace.median;
// returns 2.0

var s2 = laplace.variance;
// returns 32.0

var y = laplace.cdf( 0.8 );
// returns ~0.37

---

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.