Negative Binomial Log-Likelihood

Problem

Compute the negative binomial log likelihood for a count k with dispersion r and success probability p: lgamma(k + r) - lgamma(r) - lgamma(k + 1) + r * ln(1 - p) + k * ln(p).

Return 0.0 for invalid parameters: r <= 0, k < 0, or p outside the open interval (0, 1).

Hint

The dispersion r lets the variance exceed the mean, unlike Poisson.

Test cases

case 1

in: [0,1,0.5]

expected: -0.6931471805599453

case 2

in: [1,1,0.5]

expected: -1.3862943611198906

case 3

in: [2,2,0.5]

expected: -1.6739764335716711

case 4

in: [1,1,0]

expected: 0

Starter codePython

import math
def negative_binomial_loglik(k, r, p):
    # Your code here
    pass

4 test cases · run your code against them in the editor