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!
Gumbel distribution.
import gumbel from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-gumbel@deno/mod.js';You can also import the following named exports from the package:
import { Gumbel, cdf, entropy, kurtosis, logcdf, logpdf, mean, median, mgf, mode, pdf, quantile, skewness, stdev, variance } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-gumbel@deno/mod.js';Gumbel distribution.
var dist = gumbel;
// returns {...}The namespace contains the following distribution functions:
cdf( x, mu, beta ): Gumbel distribution cumulative distribution function.logcdf( x, mu, beta ): Gumbel distribution logarithm of cumulative distribution function.logpdf( x, mu, beta ): Gumbel distribution logarithm of probability density function (PDF).mgf( t, mu, beta ): Gumbel distribution moment-generating function (MGF).pdf( x, mu, beta ): Gumbel distribution probability density function (PDF).quantile( p, mu, beta ): Gumbel distribution quantile function.
The namespace contains the following functions for calculating distribution properties:
entropy( mu, beta ): Gumbel distribution differential entropy.kurtosis( mu, beta ): Gumbel distribution excess kurtosis.mean( mu, beta ): Gumbel distribution expected value.median( mu, beta ): Gumbel distribution median.mode( mu, beta ): Gumbel distribution mode.skewness( mu, beta ): Gumbel distribution skewness.stdev( mu, beta ): Gumbel distribution standard deviation.variance( mu, beta ): Gumbel distribution variance.
The namespace contains a constructor function for creating a Gumbel distribution object.
Gumbel( [mu, beta] ): Gumbel distribution constructor.
var Gumbel = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-gumbel' ).Gumbel;
var dist = new Gumbel( 2.0, 4.0 );
var y = dist.pdf( 2.0 );
// returns ~0.092import Float64Array from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-float64@deno/mod.js';
import filledarrayBy from 'https://cdn.jsdelivr.net/gh/stdlib-js/array-filled-by@deno/mod.js';
import mean from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-mean@deno/mod.js';
import variance from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-variance@deno/mod.js';
import stdev from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-stdev@deno/mod.js';
var randGumbel = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-gumbel' ).factory;
import gumbel from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-gumbel@deno/mod.js';
// Set the parameters of the Gumbel distribution:
var mu = 30.0; // Location parameter (e.g., average annual maximum temperature in °C)
var beta = 5.0; // Scale parameter
// Simulate annual maximum daily temperatures over 1000 years:
var N = 1000;
var rgumbel = randGumbel( mu, beta );
var maxTemperatures = filledarrayBy( N, 'float64', rgumbel );
// Compute theoretical statistics of the Gumbel distribution:
var theoreticalMean = gumbel.mean( mu, beta);
var theoreticalVariance = gumbel.variance( mu, beta );
var theoreticalStdev = gumbel.stdev( mu, beta );
// Compute sample statistics of the simulated data:
var sampleMean = mean( N, maxTemperatures, 1 );
var sampleVariance = variance( N, 1, maxTemperatures, 1 ); // with Bessel's correction
var sampleStdev = stdev( N, 1, maxTemperatures, 1 ); // with Bessel's correction
// Display theoretical and sample statistics:
console.log( '--- Statistical Comparison ---\n' );
console.log( 'Mean:');
console.log( ' Theoretical: %d°C', theoreticalMean.toFixed(2) );
console.log( ' Sample: %d°C\n', sampleMean.toFixed(2) );
console.log( 'Variance:');
console.log( ' Theoretical: %d°C²', theoreticalVariance.toFixed(2) );
console.log( ' Sample: %d°C²\n', sampleVariance.toFixed(2) );
console.log( 'Standard Deviation:' );
console.log( ' Theoretical: %d°C', theoreticalStdev.toFixed(2) );
console.log( ' Sample: %d°C\n', sampleStdev.toFixed(2) );
// Define quantile probabilities:
var p = new Float64Array( [ 0.25, 0.5, 0.75 ] );
var label = [ 'First Quartile', 'Median', 'Third Quartile' ];
var theoreticalQuantiles = new Float64Array([
gumbel.quantile( p[0], mu, beta ),
gumbel.quantile( p[1], mu, beta ),
gumbel.quantile( p[2], mu, beta )
]);
console.log( 'Quantiles:' );
var i;
for ( i = 0; i < p.length; i++ ) {
console.log( label[i] + ': %d°C', theoreticalQuantiles[i].toFixed(2) );
}This package is part of stdlib, a standard library 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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.