About stdlib...
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
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.