Poisson

Poisson distribution.

Usage

var poisson = require( '@stdlib/stats/base/dists/poisson' );

poisson

Poisson distribution.

var dist = poisson;
// returns {...}

The namespace contains the following distribution functions:

cdf( x, lambda ): Poisson distribution cumulative distribution function.
logpmf( x, lambda ): evaluate the natural logarithm of the probability mass function (PMF) for a Poisson distribution.
mgf( t, lambda ): Poisson distribution moment-generating function (MGF).
pmf( x, lambda ): Poisson distribution probability mass function (PMF).
quantile( p, lambda ): Poisson distribution quantile function.

The namespace contains the following functions for calculating distribution properties:

entropy( lambda ): Poisson distribution entropy.
kurtosis( lambda ): Poisson distribution excess kurtosis.
mean( lambda ): Poisson distribution expected value.
median( lambda ): Poisson distribution median.
mode( lambda ): Poisson distribution mode.
skewness( lambda ): Poisson distribution skewness.
stdev( lambda ): Poisson distribution standard deviation.
variance( lambda ): Poisson distribution variance.

The namespace contains a constructor function for creating a Poisson distribution object.

Poisson( [lambda] ): Poisson distribution constructor.

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 0.0

Examples

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