kstest for uniform distribution

Hi,

I have been testing the use of kstest for the detection of a discrete uniform distribution. However, I believe that I am encountering an error, or using the function incorrectly. For example, if I define a variable array

x = randi([1 4],1900,1);

where tabluate gives the following very uniform distribution

tablate(x)
 Value    Count   Percent
      1      449     23.63%
      2      482     25.37%
      3      482     25.37%
      4      487     25.63%

and I then run the test

kstest(x, 'CDF', [x unidcdf(x,4)])

I get a result of h = 1, i.e. rejection of the hypothesis that x is discrete uniform, which is clearly not the case (at least in my eyes). Would someone with more experience with this test potentially be able to helpfully provide an explanation as to why I'm getting this result? And whether I'm doing something wrong?

Many thanks.

Answer 1

[Jeff Miller]

you can test for the fit of a discrete distribution, including uniform, with chi2gof. One of the examples (about 1/3 of the way down the page) shows how to test for a Poisson distribution. With the uniform discrete, your expected counts expCounts are just the total number of observations divided by the number of possible discrete values.

[John Smith]

Thank you Jeff, that seems to do the trick well. For others that might have this problem in the future, here is the code that worked for me:

%Get a discrete uniform distribution
x = randi([1 4],1900,1);

%Create expected counts variable, which is repeated 4 times as that is the
%number of discrete values
expCounts = repmat(numel(x)/4,[4,1]);

%run the chi2gof test
[h,p,stats]=chi2gof(x,'Ctrs',[1 2 3 4],'Expected',expCounts)

%These are the results I got
h =
     0
p =
    0.5865
stats = 
  struct with fields:
    chi2stat: 1.9326
          df: 3
       edges: [0.5000 1.5000 2.5000 3.5000 4.5000]
           O: [449 482 482 487]
           E: [475 475 475 475]
           
  

As h = 0 the null hypothesis, which is that x is discrete uniform, is not rejected. I will be looking further into why the chi2 metric is suitable and the KS one is not, as this has been quite helpful!

[Jeff Miller]

Just a minor correction of the terminology at the end: the null hypothesis is that X is a discrete uniform, and h=0 means that this null hypothesis should not be rejected based on the observed X values.

[John Smith]

Thank you, I appreciate the correction, and have edited the reply to avoid anyone reading this making the same mistake.

Answer 2

[the cyclist]

From the documentation: "The one-sample Kolmogorov-Smirnov test is only valid for continuous cumulative distribution functions." (Emphasis added.)

[John Smith]

Thank you, I missed that part on the first read. I suspect Jeff Miller's answer is the way to go then, as chi square will allow for a test of discrete distributions.