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77 lines
1.6 KiB
77 lines
1.6 KiB
/**
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* Some functions for calculating distributions of random variables.
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*/
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/**
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* Takes the factorial of n.
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* @param {number} n
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* @return {number}
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*/
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const fact = n => {
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if ( n == 0 || n == 1 ) return 1
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for ( let i = n - 1; i >= 1; i -= 1 ) {
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n = n * i
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}
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return n
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}
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/**
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* Compute the {n}\choose{k} value.
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* @param {number} n the total number of items
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* @param {number} k the number to take at a time
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* @return {number}
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*/
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const choose = (n,k) => (fact(n))/(fact(k)*(fact(n-k)))
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/**
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* Calculate the binomial distribution of a random variable:
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*
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* b(x; n,p) for lower_x <= x <= upper_x
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*/
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const binom_range = (lower_x, upper_x, n, p) => {
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let sum = 0
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for ( let i = lower_x; i <= upper_x; i += 1 ) {
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sum += choose(n, i) * Math.pow(p, i) * Math.pow(1-p, n-i)
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}
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return sum
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}
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/**
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* Calculate the binomial distribution for some specific x.
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*
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* b(x; n,p)
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*/
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const binom_dist = (x, n, p) => choose(n, x) * Math.pow(p, x) * Math.pow(1-p, n-x)
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/**
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* Calculate the poisson distribution for some specific x.
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*
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* p(x, lambda * t)
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*/
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const poisson_dist = (x, lambda, t) => {
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const numerator = Math.pow(Math.E, -1 * lambda * t) * Math.pow(lambda * t, x)
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const denom = fact(x)
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return numerator / denom
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}
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/**
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* Calculate the poisson range for some specific x:
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*
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* p(x, lambda * t) for lower_x <= x <= upper_x.
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*/
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const poisson_range = (lower_x, upper_x, lambda, t) => {
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let sum = 0
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for ( let i = lower_x; i <= upper_x; i += 1 ) {
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sum += poisson_dist(i, lambda, t)
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}
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return sum
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}
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module.exports = exports = {fact, choose, binom_range, binom_dist, poisson_dist, poisson_range}
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