Poisson distribution.
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Poisson distribution.
bash
npm install @stdlib/stats-base-dists-poissonscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var poisson = require( '@stdlib/stats-base-dists-poisson' );javascript
var dist = poisson;
// returns {...}cdf( x, lambda )][@stdlib/stats/base/dists/poisson/cdf]: Poisson distribution cumulative distribution function.logpmf( x, lambda )][@stdlib/stats/base/dists/poisson/logpmf]: evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.mgf( t, lambda )][@stdlib/stats/base/dists/poisson/mgf]: Poisson distribution moment-generating function (MGF).pmf( x, lambda )][@stdlib/stats/base/dists/poisson/pmf]: Poisson distribution probability mass function (PMF).quantile( p, lambda )][@stdlib/stats/base/dists/poisson/quantile]: Poisson distribution quantile function.entropy( lambda )][@stdlib/stats/base/dists/poisson/entropy]: Poisson distribution entropy.kurtosis( lambda )][@stdlib/stats/base/dists/poisson/kurtosis]: Poisson distribution excess kurtosis.mean( lambda )][@stdlib/stats/base/dists/poisson/mean]: Poisson distribution expected value.median( lambda )][@stdlib/stats/base/dists/poisson/median]: Poisson distribution median.mode( lambda )][@stdlib/stats/base/dists/poisson/mode]: Poisson distribution mode.skewness( lambda )][@stdlib/stats/base/dists/poisson/skewness]: Poisson distribution skewness.stdev( lambda )][@stdlib/stats/base/dists/poisson/stdev]: Poisson distribution standard deviation.variance( lambda )][@stdlib/stats/base/dists/poisson/variance]: Poisson distribution variance.Poisson( [lambda] )][@stdlib/stats/base/dists/poisson/ctor]: Poisson distribution constructor.javascript
var Poisson = require( '@stdlib/stats-base-dists-poisson' ).Poisson;
var dist = new Poisson( 2.0 );
var y = dist.pmf( 3.0 );
// returns ~0.18
y = dist.pmf( 2.3 );
// returns 0.0javascript
var poisson = require( '@stdlib/stats-base-dists-poisson' );
/*
* Let's take a customer service center example: average rate of customer inquiries is 3 per hour.
* This situation can be modeled using a Poisson distribution with λ = 3
*/
var lambda = 3;
// Mean can be used to calculate the average number of inquiries per hour:
console.log( poisson.mean( lambda ) );
// => 3
// Standard deviation can be used to calculate the measure of the spread of inquiries around the mean:
console.log( poisson.stdev( lambda ) );
// => ~1.7321
// Variance can be used to calculate the variability of the number of inquiries:
console.log( poisson.variance( lambda ) );
// => 3
// PMF can be used to calculate specific number of inquiries in an hour:
console.log( poisson.pmf( 4, lambda ) );
// => ~0.1680
// CDF can be used to calculate probability up to certain number of inquiries in an hour:
console.log( poisson.cdf( 2, lambda ) );
// => ~0.4232
// Quantile can be used to calculate the number of inquiries at which you can be 80% confident that the actual number will not exceed.
console.log( poisson.quantile( 0.8, lambda ) );
// => 4
// MGF can be used for more advanced statistical analyses and generating moments of the distribution.
console.log( poisson.mgf( 1.0, lambda ) );
// => ~173.2690
