hypergeometric-distribution.js

let chance = require('chance').Chance();
let math = require('mathjs');

let newItem = function() {
	return {
		a: chance.natural({min: 1, max: 20}),
		b: chance.pickone(['alpha', 'bravo', 'charlie', 'delta', 'echo']),
		c: chance.pickset(['alpha', 'bravo', 'charlie', 'delta', 'echo'], 2),
		d: chance.natural({min: 1, max: 2}),
		sanity: 1
	}
}

let list = []

let itemCount = process.argv[2]
let setSize = process.argv[3]

for (let i = itemCount; i > 0 ; i--) {
	list.push(newItem())
}

// ugly print generated list
// process.stdout.write(JSON.stringify(list)+'\n')

// pretty print generated list
// process.stdout.write(JSON.stringify(list, undefined, 2))

// Conditions in set of list
let probabilityOfThingsInSet = (function(list, setSize){
	let conditions = [{
		filter:function(item){
			return item.d == 1
		},
		count: 1,
	}]

	// conditions are ANDed together
	return conditions.map(function(cond){
		return hypergeometricDistribution(cond.count, setSize, list.filter(cond.filter).length, list.length)
	}).reduce(function(previousValue, currentValue, currentIndex, array) {
		return previousValue * currentValue
	})
})(list, setSize)

process.stdout.write(JSON.stringify(probabilityOfThingsInSet, undefined, 2)+'\n')

// hypergeometric distribution H (X, Y) 
// H (n) = C (X, n) * C (Y - X, Z - n) / C (Y, Z)
// X stands for the number of a certain card that you have in the deck. countInList
// Y is the number of cards in the deck. listSize
// Z is the number of cards you are drawing. setSize
// N is the number you are checking for. countInSet
function hypergeometricDistribution(countInSet, setSize, countInList, listSize) {
	if (countInList < countInSet) {
		// console.log('countInSet %d, setSize %d, countInList %d, listSize %d', ...arguments)
		// console.log('countInList %d is less than countInSet %d', countInList, countInSet)
		return 1
	}
	if (listSize < setSize) {
		// console.log('countInSet %d, setSize %d, countInList %d, listSize %d', ...arguments)
		// console.log('list size %d is less than set size %d', listSize, setSize)
		return 1
	}
	if (listSize-countInList < setSize-countInSet) {
		// console.log('countInSet %d, setSize %d, countInList %d, listSize %d', ...arguments)
		// console.log('(listSize-countInList) %d is less than (setSize-countInSet) %d', listSize-countInList, setSize-countInSet)
		return 0
	}
	return math.combinations(countInList, countInSet) * math.combinations(listSize-countInList, setSize-countInSet) / math.combinations(listSize, setSize)
}