Poisson

Poisson distribution constructor.

Usage

var Poisson = require( '@stdlib/math/base/dists/poisson/ctor' );

Poisson( [lambda] )

Returns an Poisson distribution object.

var poisson = new Poisson();

var lambda = poisson.mean;
// returns 1.0

By default, lambda = 1.0. To create a distribution having a different mean parameter lambda, provide a parameter value.

var poisson = new Poisson( 4.0 );

var lambda = poisson.mean;
// returns 4.0

poisson

A Poisson distribution object has the following properties and methods...

Writable Properties

poisson.lambda

Mean parameter of the distribution. lambda must be a positive number.

var poisson = new Poisson( 2.0 );

var lambda = poisson.lambda;
// returns 2.0

poisson.lambda = 3.0;

lambda = poisson.lambda;
// returns 3.0

Computed Properties

Poisson.prototype.entropy

Returns the differential entropy.

var poisson = new Poisson( 4.0 );

var entropy = poisson.entropy;
// returns ~2.087

Poisson.prototype.kurtosis

Returns the excess kurtosis.

var poisson = new Poisson( 4.0 );

var kurtosis = poisson.kurtosis;
// returns 0.25

Poisson.prototype.mean

Returns the median.

var poisson = new Poisson( 4.0 );

var mu = poisson.mean;
// returns 4.0

Poisson.prototype.median

Returns the median.

var poisson = new Poisson( 4.0 );

var median = poisson.median;
// returns 4.0

Poisson.prototype.mode

Returns the mode.

var poisson = new Poisson( 4.0 );

var mode = poisson.mode;
// returns 4.0

Poisson.prototype.skewness

Returns the skewness.

var poisson = new Poisson( 4.0 );

var skewness = poisson.skewness;
// returns 0.5

Poisson.prototype.stdev

Returns the standard deviation.

var poisson = new Poisson( 4.0 );

var s = poisson.stdev;
// returns 2.0

Poisson.prototype.variance

Returns the variance.

var poisson = new Poisson( 4.0 );

var s2 = poisson.variance;
// returns 4.0

Methods

Poisson.prototype.cdf( x )

Evaluates the cumulative distribution function (CDF).

var poisson = new Poisson( 2.0 );

var y = poisson.cdf( 0.5 );
// returns ~0.135

Poisson.prototype.logpmf( x )

Evaluates the natural logarithm of the probability mass function (PMF).

var poisson = new Poisson( 2.0 );

var y = poisson.logpmf( 3.0 );
// returns ~-1.715

y = poisson.logpmf( 2.3 );
// returns -Infinity

Poisson.prototype.mgf( t )

Evaluates the moment-generating function (MGF).

var poisson = new Poisson( 2.0 );

var y = poisson.mgf( 0.5 );
// returns ~3.66

Poisson.prototype.pmf( x )

Evaluates the probability mass function (PMF).

var poisson = new Poisson( 2.0 );

var y = poisson.pmf( 3.0 );
// returns ~0.18

y = poisson.pmf( 2.3 );
// returns 0.0

Poisson.prototype.quantile( p )

Evaluates the quantile function at probability p.

var poisson = new Poisson( 2.0 );

var y = poisson.quantile( 0.5 );
// returns 2.0

y = quantile( 1.9 );
// returns NaN

Examples

var Poisson = require( '@stdlib/math/base/dists/poisson/ctor' );

var poisson = new Poisson( 2.0 );

var mu = poisson.mean;
// returns 2.0

var mode = poisson.mode;
// returns 2.0

var s2 = poisson.variance;
// returns 2.0

var y = poisson.cdf( 0.8 );
// returns ~0.135