Binomial

Binomial distribution.

Usage

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

binomial

Binomial distribution.

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

The namespace contains the following distribution functions:

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

The namespace contains the following functions for calculating distribution properties:

entropy( n, p ): binomial distribution entropy.
kurtosis( n, p ): binomial distribution excess kurtosis.
mean( n, p ): binomial distribution expected value.
median( n, p ): binomial distribution median.
mode( n, p ): binomial distribution mode.
skewness( n, p ): binomial distribution skewness.
stdev( n, p ): binomial distribution standard deviation.
variance( n, p ): binomial distribution variance.

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

Binomial( [n, p] ): binomial distribution constructor.

var Binomial = require( '@stdlib/stats/base/dists/binomial' ).Binomial;
var dist = new Binomial( 10, 0.4 );

var mu = dist.mean;
// returns 4

Examples

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

/*
* Let's take an example of rolling a fair dice 10 times and counting the number of times a 6 is rolled.
* This situation can be modeled using a Binomial distribution with n = 10 and p = 1/6
*/

var n = 10;
var p = 1/6;

// Mean can be used to calculate the average number of times a 6 is rolled:
console.log( binomial.mean( n, p ) );
// => ~1.6667

// PMF can be used to calculate the probability of getting a certain number of 6s (say 3 sixes):
console.log( binomial.pmf( 3, n, p ) );
// => ~0.1550

// CDF can be used to calculate probability up to certain number of 6s (say up to 3 sixes):
console.log( binomial.cdf( 3, n, p ) );
// => ~0.9303

// Quantile can be used to calculate the number of 6s at which you can be 80% confident that the actual number will not exceed.
console.log( binomial.quantile( 0.8, n, p ) );
// => 3

// Standard deviation can be used to calculate the measure of the spread of 6s around the mean:
console.log( binomial.stdev( n, p ) );
// => ~1.1785

// Skewness can be used to calculate the asymmetry of the distribution of 6s:
console.log( binomial.skewness( n, p ) );
// => ~0.5657

// MGF can be used for more advanced statistical analyses and generating moments of the distribution:
console.log( binomial.mgf( 0.5, n, p ) );
// => ~2.7917