multinomial-pmf

multinomial probability mass function

installation

npm install multinomial-pmf

usage

var multpmf = require('multinomial-pmf')
multpmf([0.5,0.5], [1,1]) // coin toss: HT
// 0.5
multpmf([0.5,0.5], [0,3]) // coin toss: TTT
// 0.125
var diceProbs = [1,1,1,1,1,1].map(function(x) { return x/6 })
multpmf(diceProbs, [1,2,0,3,0,1]) // fair six-sided die
// 0.0015003429355281205

There is also a log-space (but approximate) version:

var logmultpmf = require('multinomial-pmf').log
logmultpmf([0.5, 0.5], [2, 3])
// -1.163150809805681
Math.exp(logmultpmf([0.5, 0.5], [2, 3]))
// 0.31249999999999994

You'll incur some (small) loss of precision using the log version, but also you'll be able to handle much more complex multinomial distributions.

overview

This module calculates the discrete sampling probability of a multiset of a given size from an underlying source multinomial distribution. In other words, it implements the multinomial probability mass function.

It helps us answer questions like:

• If I have 5 red, 3 blue, and 1 yellow ball in a bag, what's the probability that I draw 3 blue and 1 red (with replacement, in other words, the balls go back in the back after I've pulled them)?

var bag   = [5,3,1]
var pulls = [1,3,0]

function countsToProbs(counts) {
    var sum = counts.reduce(function(x,y) { return x+y })
    return counts.map(function(x) { return x/sum })
}

multpmf(countsToProbs(bag), pulls)
// 0.0823045267489712

The binomial distribution is a special case of the multinomial where the number of categories is 2.

license

MIT