mathjs/src/plain/number/probability.js

Math.js is an extensive math library for JavaScript and Node.js. It features a flexible expression parser with support for symbolic computation, comes with a large set of built-in functions and constants, and offers an integrated solution to work with dif

import { isInteger } from '../../utils/number'
import { product } from '../../utils/product'

export function gammaNumber (n) {
  let x

  if (isInteger(n)) {
    if (n <= 0) {
      return isFinite(n) ? Infinity : NaN
    }

    if (n > 171) {
      return Infinity // Will overflow
    }

    return product(1, n - 1)
  }

  if (n < 0.5) {
    return Math.PI / (Math.sin(Math.PI * n) * gammaNumber(1 - n))
  }

  if (n >= 171.35) {
    return Infinity // will overflow
  }

  if (n > 85.0) { // Extended Stirling Approx
    const twoN = n * n
    const threeN = twoN * n
    const fourN = threeN * n
    const fiveN = fourN * n
    return Math.sqrt(2 * Math.PI / n) * Math.pow((n / Math.E), n) *
      (1 + 1 / (12 * n) + 1 / (288 * twoN) - 139 / (51840 * threeN) -
        571 / (2488320 * fourN) + 163879 / (209018880 * fiveN) +
        5246819 / (75246796800 * fiveN * n))
  }

  --n
  x = gammaP[0]
  for (let i = 1; i < gammaP.length; ++i) {
    x += gammaP[i] / (n + i)
  }

  const t = n + gammaG + 0.5
  return Math.sqrt(2 * Math.PI) * Math.pow(t, n + 0.5) * Math.exp(-t) * x
}
gammaNumber.signature = 'number'

// TODO: comment on the variables g and p

export const gammaG = 4.7421875

export const gammaP = [
  0.99999999999999709182,
  57.156235665862923517,
  -59.597960355475491248,
  14.136097974741747174,
  -0.49191381609762019978,
  0.33994649984811888699e-4,
  0.46523628927048575665e-4,
  -0.98374475304879564677e-4,
  0.15808870322491248884e-3,
  -0.21026444172410488319e-3,
  0.21743961811521264320e-3,
  -0.16431810653676389022e-3,
  0.84418223983852743293e-4,
  -0.26190838401581408670e-4,
  0.36899182659531622704e-5
]