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

Pareto (Type I) distribution constructor.

https://github.com/stdlib-js/stats-base-dists-pareto-type1-ctor

Science Score: 44.0%

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class constructor ctor dist distribution economics finance javascript node node-js nodejs object pareto prob probability risk statistics stats stdlib tail

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Repository

Pareto (Type I) distribution constructor.

Basic Info

Host: GitHub
Owner: stdlib-js
License: apache-2.0
Language: JavaScript
Default Branch: main
Homepage: https://github.com/stdlib-js/stdlib
Size: 2.12 MB

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class constructor ctor dist distribution economics finance javascript node node-js nodejs object pareto prob probability risk statistics stats stdlib tail

Created over 4 years ago · Last pushed 8 months ago

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Readme Changelog Contributing License Code of conduct Citation Security

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 ```bash npm install @stdlib/stats-base-dists-pareto-type1-ctor ``` Alternatively, - To load the package in a website via a `script` tag without installation and bundlers, use the [ES Module][es-module] available on the [`esm`][esm-url] branch (see [README][esm-readme]). - If you are using Deno, visit the [`deno`][deno-url] branch (see [README][deno-readme] for usage intructions). - For use in Observable, or in browser/node environments, use the [Universal Module Definition (UMD)][umd] build available on the [`umd`][umd-url] branch (see [README][umd-readme]). The [branches.md][branches-url] 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 ```javascript var Pareto1 = require( '@stdlib/stats-base-dists-pareto-type1-ctor' ); ``` #### Pareto1( \[alpha, beta] ) Returns a [Pareto (Type I)][pareto-distribution] distribution object. ```javascript 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. ```javascript var pareto1 = new Pareto1( 2.0, 4.0 ); var mu = pareto1.mean; // returns 8.0 ``` * * * ## pareto1 A [Pareto (Type I)][pareto-distribution] distribution object has the following properties and methods... ### Writable Properties #### pareto1.alpha Shape parameter of the distribution. `alpha` **must** be a positive number. ```javascript 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. ```javascript 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][entropy]. ```javascript var pareto1 = new Pareto1( 4.0, 12.0 ); var entropy = pareto1.entropy; // returns ~2.349 ``` #### Pareto1.prototype.kurtosis Returns the [excess kurtosis][kurtosis]. ```javascript var pareto1 = new Pareto1( 6.0, 12.0 ); var kurtosis = pareto1.kurtosis; // returns ~35.667 ``` #### Pareto1.prototype.mean Returns the [expected value][expected-value]. ```javascript var pareto1 = new Pareto1( 4.0, 12.0 ); var mu = pareto1.mean; // returns 16.0 ``` #### Pareto1.prototype.median Returns the [median][median]. ```javascript var pareto1 = new Pareto1( 4.0, 12.0 ); var median = pareto1.median; // returns ~14.27 ``` #### Pareto1.prototype.mode Returns the [mode][mode]. ```javascript var pareto1 = new Pareto1( 4.0, 12.0 ); var mode = pareto1.mode; // returns 12.0 ``` #### Pareto1.prototype.skewness Returns the [skewness][skewness]. ```javascript var pareto1 = new Pareto1( 4.0, 12.0 ); var skewness = pareto1.skewness; // returns ~7.071 ``` #### Pareto1.prototype.variance Returns the [variance][variance]. ```javascript 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] (CDF). ```javascript 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] (CDF). ```javascript 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] (PDF). ```javascript 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] (PDF). ```javascript 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][quantile-function] at probability `p`. ```javascript 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 ```javascript 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][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][stdlib], see the main project [repository][stdlib]. #### Community [![Chat][chat-image]][chat-url] --- ## License See [LICENSE][stdlib-license]. ## Copyright Copyright © 2016-2025. The Stdlib [Authors][stdlib-authors].

Owner

Name: stdlib
Login: stdlib-js
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Website: https://stdlib.io
Twitter: stdlibjs
Repositories: 3,692
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Standard library for JavaScript.

Citation (CITATION.cff)

cff-version: 1.2.0
title: stdlib
message: >-
  If you use this software, please cite it using the
  metadata from this file.

type: software

authors:
  - name: The Stdlib Authors
    url: https://github.com/stdlib-js/stdlib/graphs/contributors

repository-code: https://github.com/stdlib-js/stdlib
url: https://stdlib.io

abstract: |
  Standard library for JavaScript and Node.js.

keywords:
  - JavaScript
  - Node.js
  - TypeScript
  - standard library
  - scientific computing
  - numerical computing
  - statistical computing

license: Apache-2.0 AND BSL-1.0

date-released: 2016

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npmjs.org: @stdlib/stats-base-dists-pareto-type1-ctor

Pareto (Type I) distribution constructor.

Homepage: https://stdlib.io
License: Apache-2.0
Latest release: 0.2.2
published over 1 year ago

Versions: 12
Dependent Packages: 5
Dependent Repositories: 3
Downloads: 43 Last month

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@stdlib/assert-has-own-property ^0.0.x development
@stdlib/assert-is-function ^0.0.x development
@stdlib/bench ^0.0.x development
@stdlib/constants-float64-eps ^0.0.x development
@stdlib/math-base-assert-is-nan ^0.0.x development
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istanbul ^0.4.1 development
tap-spec 5.x.x development
tape git+https://github.com/kgryte/tape.git#fix/globby development
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@stdlib/stats-base-dists-pareto-type1-cdf ^0.0.x
@stdlib/stats-base-dists-pareto-type1-entropy ^0.0.x
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@stdlib/stats-base-dists-pareto-type1-logcdf ^0.0.x
@stdlib/stats-base-dists-pareto-type1-logpdf ^0.0.x
@stdlib/stats-base-dists-pareto-type1-mean ^0.0.x
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@stdlib/stats-base-dists-pareto-type1-mode ^0.0.x
@stdlib/stats-base-dists-pareto-type1-pdf ^0.0.x
@stdlib/stats-base-dists-pareto-type1-quantile ^0.0.x
@stdlib/stats-base-dists-pareto-type1-skewness ^0.0.x
@stdlib/stats-base-dists-pareto-type1-variance ^0.0.x
@stdlib/string-format ^0.0.x
@stdlib/utils-define-nonenumerable-read-only-accessor ^0.0.x
@stdlib/utils-define-nonenumerable-read-only-property ^0.0.x
@stdlib/utils-define-property ^0.0.x

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

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