/**
 * Some functions for calculating distributions of random variables.
 */

/**
 * Takes the factorial of n.
 * @param {number} n
 * @return {number}
 */
const fact = n => {
    if ( n == 0 || n == 1 ) return 1

    for ( let i = n - 1; i >= 1; i -= 1 ) {
        n = n * i
    }

    return n
}

/**
 * Compute the {n}\choose{k} value.
 * @param {number} n the total number of items
 * @param {number} k the number to take at a time
 * @return {number}
 */
const choose = (n,k) => (fact(n))/(fact(k)*(fact(n-k)))

/**
 * Calculate the binomial distribution of a random variable:
 *
 * b(x; n,p) for lower_x <= x <= upper_x
 */
const binom_range = (lower_x, upper_x, n, p) => {
    let sum = 0

    for ( let i = lower_x; i <= upper_x; i += 1 ) {
        sum += choose(n, i) * Math.pow(p, i) * Math.pow(1-p, n-i)
    }

    return sum
}

/**
 * Calculate the binomial distribution for some specific x.
 *
 * b(x; n,p)
 */
const binom_dist = (x, n, p) => choose(n, x) * Math.pow(p, x) * Math.pow(1-p, n-x)

/**
 * Calculate the poisson distribution for some specific x.
 *
 * p(x, lambda * t)
 */
const poisson_dist = (x, lambda, t) => {
    const numerator = Math.pow(Math.E, -1 * lambda * t) * Math.pow(lambda * t, x)
    const denom = fact(x)
    return numerator / denom
}

/**
 * Calculate the poisson range for some specific x:
 *
 * p(x, lambda * t) for lower_x <= x <= upper_x.
 */
const poisson_range = (lower_x, upper_x, lambda, t) => {
    let sum = 0

    for ( let i = lower_x; i <= upper_x; i += 1 ) {
        sum += poisson_dist(i, lambda, t)
    }

    return sum
}

module.exports = exports = {fact, choose, binom_range, binom_dist, poisson_dist, poisson_range}