Cantelli Bound Value

Problem

Cantelli's one-sided inequality bounds P(X - mean >= a) by variance / (variance + a^2) for a > 0. Return the bound, 1.0 for a <= 0, and 0.0 when the variance is nonpositive.

Hint

The bound interpolates smoothly between 0 and 1 as a grows.

Test cases

case 1

in: [1,1]

expected: 0.5

case 2

in: [1,2]

expected: 0.2

case 3

in: [4,2]

expected: 0.5

case 4

in: [0,1]

expected: 0

case 5

in: [1,0]

expected: 1

Starter codePython

def cantelli_bound(variance, a):
    # Your code here
    pass

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