Branching Process Extinction Probability

Problem

Probability that a branching process dies out, given the offspring distribution probs (probs[k] = P(k offspring)). The extinction probability is the smallest fixed point q of q = sum(probs[k] * q^k), found by iterating from 0. Return 1.0 when the mean offspring number is at most 1 or the distribution is empty.

Hint

Start from q = 0 and use the fact that the extinction probability is the smallest fixed point.

Test cases

case 1

in: [[0.25,0.5,0.25]]

expected: 1

case 2

in: [[0.2,0.3,0.5]]

expected: 0.3999999999997775

case 3

in: [[0.1,0.2,0.3,0.4]]

expected: 0.13278221853728808

case 4

in: [[1]]

expected: 1

case 5

in: [[0.5,0.5]]

expected: 1

Starter codePython

def branching_extinction_probability(probs):
    # Your code here
    pass

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