Erlang PDF (Convolution of Exponentials)

Problem

The sum of n independent Exponential(lam) variables is Erlang distributed. Return its density at x:

f(x) = lam^n * x^(n - 1) * e^(-lam * x) / (n - 1)! for x >= 0.

Return 0.0 for nonpositive lam, n < 1 or x < 0.

Hint

Convolving exponential densities n times gives the Erlang shape.

case 1

in: [1,1,1]

expected: 0.36787944117144233

case 2

in: [2,2,1]

expected: 0.5413411329464508

case 3

in: [1,3,2]

expected: 0.2706705664732254

case 4

in: [1,1,0]

expected: 1

Starter codePython

import math


def erlang_pdf(lam, n, x):
    # Your code here
    pass

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