Stationary Birth-Death Probabilities

Problem

Stationary distribution of a birth-death chain on states 0..N. births[i] is the rate from state i to i + 1 and deaths[i] is the rate from state i + 1 down to i. Build pi[i + 1] = pi[i] * births[i] / deaths[i], then normalize. Return a list of probabilities, or [] when the lists are empty or mismatched or a death rate is nonpositive.

Hint

Detailed balance gives the ratio of neighboring stationary probabilities.

Test cases

case 1

in: [[0.5,0.5],[0.5,0.5]]

expected: [0.3333333333333333,0.3333333333333333,0.3333333333333333]

case 2

in: [[1,2],[2,1]]

expected: [0.4,0.2,0.4]

case 3

in: [[1,1,1],[1,1,1]]

expected: [0.25,0.25,0.25,0.25]

case 4

in: [[],[]]

expected: []

Starter codePython

def stationary_birth_death(births, deaths):
    # Your code here
    pass

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