Dirichlet Coordinate Variance

Problem

The marginal distribution of coordinate i of a Dirichlet(alphas) variable is Beta with parameters (alphas[i], A - alphas[i]), where A = sum(alphas). Return its variance alphas[i] * (A - alphas[i]) / (A^2 * (A + 1)). Return 0.0 for an empty vector, an out-of-range index, or any nonpositive concentration.

Hint

Use the Beta variance formula on the i-th marginal distribution.

Test cases

case 1

in: [[1,1],0]

expected: 0.08333333333333333

case 2

in: [[2,3,5],2]

expected: 0.022727272727272728

case 3

in: [[1,1,1,1],0]

expected: 0.0375

case 4

in: [[2,2],1]

expected: 0.05

case 5

in: [[1,2],5]

expected: 0

Starter codePython

def dirichlet_coordinate_variance(alphas, i):
    # Your code here
    pass

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