Kling-Gupta Efficiency

Problem

Compute the Kling-Gupta efficiency: 1 - sqrt((r - 1)^2 + (alpha - 1)^2 + (beta - 1)^2), where r is the Pearson correlation, alpha = std_forecast / std_actual, and beta = mean_forecast / mean_actual, all with population moments.

Return 0.0 when the lists are empty, mismatched, or any reference moment is zero.

Hint

The score decomposes into correlation, variability, and bias components.

Test cases

case 1

in: [[1,2,3,4],[1,2,3,4]]

expected: 0.9999999999999998

case 2

in: [[1,2,3,4],[2,2,2,2]]

expected: 0

case 3

in: [[1,2,3],[1,3,2]]

expected: 0.5000000000000001

case 4

in: [[2,4,6],[4,8,12]]

expected: -0.41421356237309515

Starter codePython

def kling_gupta_efficiency(actual, forecast):
    # Your code here
    pass

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