Calibration Set Size Effect

Problem

Estimate calibration range underestimation: with num_samples samples the expected maximum of a uniform range misses the true max by true_max / (num_samples + 1). A non-positive sample count returns true_max.

The signature is calibration_range_error(true_max, num_samples).

Hint

The expected maximum of n uniform samples is M*n/(n+1), leaving an M/(n+1) gap.

Test cases

case 1

in: [10,99]

expected: 0.1

case 2

in: [5,4]

expected: 1

case 3

in: [1,0]

expected: 1

case 4

in: [3,9]

expected: 0.3

Starter codePython

def calibration_range_error(true_max, num_samples):
    # Your code here
    pass

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