how to test if multiple distributions are statistically different from each other?

Hello,

I have four systems that have lognormal distributions as follows:

I want to know if these four lognormal distributions are statistcally different from each other. How do I do that in Matlab?

Answer 1

[the cyclist]

What is reported in that table are the parameters of lognormal distributions. Because the parameters are different, those distributions are different from each other. There is no statistics here.

If you have data from two distributions (where you do not know the generating parameters), then you can use kstest2 to test whether those data were drawn from the same underlying continuous distribution.

[Masih Alavy]

I have data for the four (4) distributions. I want to compare the 4 sets of data and see if they are statistically different or not. My problem is that I have 4 sets of data (not 2 sets) and that's why I cannot use the kstest2. Could you please shed some light?

[the cyclist]

You have a very specific problem. I don't expect there to be a built-in function that will do exactly what you want.

The first thing you need to do is get specific about exactly what hypothesis you are testing. Is your null hypothesis that all the data is from a single distribution, and you are trying to reject that hypothesis? You might still be able to use kstest2, in pairwise fashion.