Thinning of a Poisson Process

Problem

Each event of a Poisson process with rate lam is independently kept with probability p. Return the probability that exactly k kept events occur in time t.

The thinned process is Poisson with rate lam * p. Return 0.0 for invalid probabilities or negative inputs.

Hint

Independent thinning preserves the Poisson property with a reduced rate.

Test cases

case 1

in: [2,0.5,2,1]

expected: 0.2706705664732254

case 2

in: [3,1,1,2]

expected: 0.22404180765538775

case 3

in: [5,0,1,0]

expected: 1

case 4

in: [1,2,1,1]

expected: 0

Starter codePython

import math


def thinning_poisson_probability(lam, p, t, k):
    # Your code here
    pass

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