weibull:威布尔分布

Weibull === [![NPM version][npm-image]][npm-url] [![Build Status][travis-image]][travis-url] [![Coverage Status][coveralls-image]][coveralls-url] [![Dependencies][dependencies-image]][dependencies-url] > Weibull distribution. ## Installation ``` bash $ npm install distributions-weibull ``` For use in the browser, use [browserify](https://github.com/substack/node-browserify). ## Usage ``` javascript var createDist = require( 'distributions-weibull' ); ``` To create a Weibull distribution, ``` javascript var dist = createDist(); ``` The constructor function takes two input arguments, `lambda` and `k`, the shape and scale parameters of the Weibull distribution. By default, a distribution with `lambda = 1` and `k = 1` is created. The distribution is configurable and has the following methods... #### dist.support() Returns the distribution support, which is all numbers in the interval `(0,∞)`. ``` javascript var support = dist.support(); // returns [ 0,+Infinity ] ``` #### dist.lambda( [value] ) This method is a setter/getter. If no `value` is provided, returns the shape parameter `lambda`. To set `lambda`, ``` javascript dist.lambda( 10 ); ``` The default shape parameter is 1. #### dist.k( [value] ) This method is a setter/getter. If no `value` is provided, returns the scale parameter `k`. To set `k`, ``` javascript dist.k( 100 ); ``` The default scale parameter is 1. #### dist.mean() Returns the distribution `mean`. ``` javascript var mean = dist.mean(); ``` #### dist.variance() Returns the distribution `variance`. ``` javascript var variance = dist.variance(); ``` #### dist.median() Returns the distribution `median`. ``` javascript var median = dist.median(); ``` #### dist.skewness() Returns the distribution `skewness`. ``` javascript var skewness = dist.skewness(); ``` #### dist.ekurtosis() Returns the distribution `excess kurtosis`. ``` javascript var excess = dist.ekurtosis(); ``` #### dist.entropy() Returns the distribution's [differential entropy](http://en.wikipedia.org/wiki/Differential_entropy). ``` javascript var entropy = dist.entropy(); ``` #### dist.pdf( [x] ) If no argument is provided, returns the probability density function (PDF). If a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix) is provided, evaluates the PDF for each element. ``` javascript var data = [ 0, 0.2, 0.5, 0.8 ]; var pdf = dist.pdf( data ); // returns [...] ``` #### dist.cdf( [x] ) If no argument is provided, returns the cumulative distribution function (CDF). If a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix) is provided, evaluates the CDF for each element. ``` javascript var data = [ 0, 0.2, 0.5, 0.8 ]; var cdf = dist.cdf( data ); // returns [...] ``` #### dist.quantile( [p] ) If no argument is provided, returns the inverse cumulative distribution (quantile) function. If a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix) of probabilities is provided, evaluates the quantile function for each element. ``` javascript var probs = [ 0.025, 0.5, 0.975 ]; var quantiles = dist.quantile( probs ); // returns [...] ``` Note: all values must exist on the interval `[0, 1]`. The function returns `NaN` for a value not satisfying this condition. #### dist.mgf( [t] ) If no argument is provided, returns the moment generating function (MGF) of the distribution. If a [`number`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Number), an [`array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array), a [`typed array`](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays), or a [`matrix`](https://github.com/dstructs/matrix) is provided, evaluates the MGF for each input element. ## Examples ``` javascript var createDist = require( 'distributions-weibull' ); // Define the distribution parameters... var lambda = 10, k = 20; // Create a vector... var vec = new Array( 1000 ), len = vec.length; for ( var i = 0; i < len; i++ ) { vec[ i ] = lambda * Math.pow( -Math.log( 1 - Math.random() ) , 1/k ); } // Create a Weibull distribution and configure... var dist = createDist( lambda, k ); // Evaluate the probability density function over the vector... var pdf = dist.pdf( vec ); var arr = new Array( 100 ); for ( var j = 0; j < arr.length; j++ ) { arr[ j ] = [ vec[j], pdf[j] ]; } console.log( arr ); // Evaluate the quantile function for canonical cumulative probability values... var quantiles = dist.quantile( [ 0.025, 0.5, 0.975 ] ); console.log( quantiles ); ``` To run the example code from the top-level application directory, ``` bash $ node ./examples/index.js ``` ## Tests ### Unit Unit tests use the [Mocha](http://mochajs.org) test framework with [Chai](http://chaijs.com) assertions. To run the tests, execute the following command in the top-level application directory: ``` bash $ make test ``` All new feature development should have corresponding unit tests to validate correct functionality. ### Test Coverage This repository uses [Istanbul](https://github.com/gotwarlost/istanbul) as its code coverage tool. To generate a test coverage report, execute the following command in the top-level application directory: ``` bash $ make test-cov ``` Istanbul creates a `./reports/coverage` directory. To access an HTML version of the report, ``` bash $ open reports/coverage/lcov-report/index.html ``` --- ## License [MIT license](http://opensource.org/licenses/MIT). ## Copyright Copyright &copy; 2015. The [Distributions.io](https://github.com/distributions-io) Authors. [npm-image]: http://img.shields.io/npm/v/distributions-weibull.svg [npm-url]: https://npmjs.org/package/distributions-weibull [travis-image]: http://img.shields.io/travis/distributions-io/weibull/master.svg [travis-url]: https://travis-ci.org/distributions-io/weibull [coveralls-image]: https://img.shields.io/coveralls/distributions-io/weibull/master.svg [coveralls-url]: https://coveralls.io/r/distributions-io/weibull?branch=master [dependencies-image]: http://img.shields.io/david/distributions-io/weibull.svg [dependencies-url]: https://david-dm.org/distributions-io/weibull [dev-dependencies-image]: http://img.shields.io/david/dev/distributions-io/weibull.svg [dev-dependencies-url]: https://david-dm.org/dev/distributions-io/weibull [github-issues-image]: http://img.shields.io/github/issues/distributions-io/weibull.svg [github-issues-url]: https://github.com/distributions-io/weibull/issues