Two-Sample Kolmogorov-Smirnov Test Statistic

Hi,

Matlab kstest2 function computes the Kolmogorov-Smirnov Test Statistic as:

D* = max x (|F1(x) - F2(x)|)

where F1(x) is the proportion of x1 values less than or equal to x and F2(x) is the proportion of x2 values less than or equal to x.

However, I need to compute the Kolmogorov-Smirnov Test Statistic as:

D* = ( (n1*n2) / (n1+n2) )^(1/2) * max x (| (1/n1)*F1(x) - (1/n2)*F2(x) |)

where n1 and n2 are x1 and x2 samples sizes, respectively.

Could you please help me with the code to do this?

Thanks in advance!

Answer 1

[Aditya]

Hi Barbara ,

In order to compute the Kolmogorov-Smirnov test statistic as you've described, you can use the following MATLAB code. This code calculates the statistic using your specified formula:

function D_star = custom_kstest2(x1, x2)
    % Sort the samples
    x1 = sort(x1);
    x2 = sort(x2);
    
    % Sample sizes
    n1 = length(x1);
    n2 = length(x2);
    
    % Combined sample
    combined_sample = unique([x1; x2]);

    % Initialize the empirical distribution functions
    F1 = zeros(size(combined_sample));
    F2 = zeros(size(combined_sample));

    % Calculate the empirical distribution functions
    for i = 1:length(combined_sample)
        F1(i) = sum(x1 <= combined_sample(i)) / n1;
        F2(i) = sum(x2 <= combined_sample(i)) / n2;
    end

    % Calculate the maximum difference
    max_diff = max(abs(F1 - F2));

    % Calculate the modified Kolmogorov-Smirnov statistic
    D_star = sqrt((n1 * n2) / (n1 + n2)) * max_diff;
end

% Example usage:
x1 = [1, 2, 3, 4, 5];
x2 = [2, 3, 4, 5, 6];
D_star = custom_kstest2(x1, x2);
disp(D_star);

Hope, this helps.