Pareto (Type I)

Pareto (Type I) distribution constructor.

Installation

npm install @stdlib/stats-base-dists-pareto-type1-ctor

Usage

var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' );

Pareto1( [alpha, beta] )

Returns a Pareto (Type I) distribution object.

var pareto1 = new Pareto1();

var mu = pareto1.mean;
// returns Infinity

By default, alpha = 1.0 and beta = 1.0. To create a distribution having a different alpha (shape parameter) and beta (scale parameter), provide the corresponding arguments.

var pareto1 = new Pareto1( 2.0, 4.0 );

var mu = pareto1.mean;
// returns 8.0

pareto1

A Pareto (Type I) distribution object has the following properties and methods...

Writable Properties

pareto1.alpha

Shape parameter of the distribution. alpha must be a positive number.

var pareto1 = new Pareto1();

var alpha = pareto1.alpha;
// returns 1.0

pareto1.alpha = 3.0;

alpha = pareto1.alpha;
// returns 3.0

pareto1.beta

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

var pareto1 = new Pareto1( 2.0, 4.0 );

var beta = pareto1.beta;
// returns 4.0

pareto1.beta = 3.0;

beta = pareto1.beta;
// returns 3.0

Computed Properties

Pareto1.prototype.entropy

Returns the differential entropy.

var pareto1 = new Pareto1( 4.0, 12.0 );

var entropy = pareto1.entropy;
// returns ~2.349

Pareto1.prototype.kurtosis

Returns the excess kurtosis.

var pareto1 = new Pareto1( 6.0, 12.0 );

var kurtosis = pareto1.kurtosis;
// returns ~35.667

Pareto1.prototype.mean

Returns the expected value.

var pareto1 = new Pareto1( 4.0, 12.0 );

var mu = pareto1.mean;
// returns 16.0

Pareto1.prototype.median

Returns the median.

var pareto1 = new Pareto1( 4.0, 12.0 );

var median = pareto1.median;
// returns ~14.27

Pareto1.prototype.mode

Returns the mode.

var pareto1 = new Pareto1( 4.0, 12.0 );

var mode = pareto1.mode;
// returns 12.0

Pareto1.prototype.skewness

Returns the skewness.

var pareto1 = new Pareto1( 4.0, 12.0 );

var skewness = pareto1.skewness;
// returns ~7.071

Pareto1.prototype.variance

Returns the variance.

var pareto1 = new Pareto1( 4.0, 12.0 );

var s2 = pareto1.variance;
// returns 32.0

Methods

Pareto1.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.cdf( 3.5 );
// returns 0.0

Pareto1.prototype.logcdf( x )

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

var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.logcdf( 3.5 );
// returns -Infinity

Pareto1.prototype.logpdf( x )

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

var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.logpdf( 5.0 );
// returns ~-1.363

Pareto1.prototype.pdf( x )

Evaluates the probability density function (PDF).

var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.pdf( 5.0 );
// returns ~0.256

Pareto1.prototype.quantile( p )

Evaluates the quantile function at probability p.

var pareto1 = new Pareto1( 2.0, 4.0 );

var y = pareto1.quantile( 0.5 );
// returns ~5.657

y = pareto1.quantile( 1.9 );
// returns NaN

Examples

var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' );

var pareto1 = new Pareto1( 2.0, 4.0 );

var mu = pareto1.mean;
// returns 8.0

var median = pareto1.median;
// returns ~5.657

var s2 = pareto1.variance;
// returns Infinity

var y = pareto1.cdf( 2.0 );
// returns 0.0

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

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.