working with kolmogrov test
Hi, I am trying to use kolmogorov test which I' going to use it in my artickle , I generate a data set A then I randomly made a sample set from A. then I wanated to compare these two sample sets with kstest. but It showed me they don't have same distribution. here is my simple code: clc clear all close all n_s = 1000; mother_random_variable = lognrnd(0.3,0.5,[1,100000]); %data lognormal S = mother_random_variable(randi(numel(mother_random_variable),1,n_s)) %sample S_y = [S]'; %selected data S_mean=mean(S_y); %mean sample S_var=std(S_y); %variance sammple test_cdf = [S_y,cdf('Lognormal',S_y,S_var,S_mean)]; %make cdf kstest(S_y,'CDF',test_cdf) %ktest plot(sort(S_y),logncdf(sort(S_y)),'r--') hold on cdfplot(S_y) they have same distribution and ITs srange result . I found more strage result when I compare my data set with itself, Its result shows me they don't have same distribution. clc clear all close all n_s = 1000; mother_random_variable = lognrnd(0.3,0.5,[1,100000]); %data S=mother_random_variable; % I named data with S for simpler code S_y = [S]'; %selected data S_mean=mean(S_y); S_var=std(S_y); test_cdf = [S_y,cdf('Lognormal',S_y,S_var,S_mean)]; kstest(S_y,'CDF',test_cdf) plot(sort(S_y),logncdf(sort(S_y)),'r--') hold on cdfplot(S_y) DO you have any Idea.
Prashant Kumar answered .
2025-11-20
y = cdf('Lognormal', S_y, S_var, S_mean); % your code, incorrect
y = cdf('Lognormal', S_y, S_mean, S_var); % correct
2) This is just a suggestion but it's a bit cleaner to use the makedist() function rather than entering the parameters manually into cdf().
doc cdf
pd = makedist('Lognormal', 'mu', S_mean, 'sigma', S_var);
y = cdf(pd, S_y); % instead of cdf('Lognormal', S_y, S_mean, S_var)
3) " when I compare my data set with itself, Its result shows me they don't have same distribution." But you aren't comparing your data with itself. You're comparing your data with the results of the cumulative distribution function of your data. The plot below shows the distribution of values from your data (top) and the distribution of values from the CDF. Clearly those distributions differ and the kstest() correctly rejects the null hypothesis.
figure
subplot(2,1,1)
histogram(S_y)
title('mother random variable')
subplot(2,1,2)
histogram(cdf('Lognormal', S_y, S_mean, S_var))
title('CDF distribution')
