different in Poisson distribution test

I have a problem when i take a test of poisson distribution. I have the data: 0, 1, 2, 0, 3, 2, 1, 2, 1, 0, 1, 2, 3, 2, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 1, 3, 2, 0, 1, 1, 2, 1, 1. I test is wonder the data have Poisson distribution. I use 3 ways:

1. >> dl=[0, 1, 2, 0, 3, 2, 1, 2, 1, 0, 1, 2, 3, 2, 1, 1, 0, 1, 2, 3, 1, 0, 1, 1, 2, 1, 2, 1, 0, 1, 2, 1, 3, 2, 0, 1, 1, 2, 1, 1];

>> x=unique(dl);

>> ts=histcounts(dl);

>> [h,p]=chi2gof(dl,'CDF',makedist('Poisson',mean(dl)))

the results are: h = 0 p = 0.9810

2. >> n=length(dl);

>> tslt=n*pdf(makedist('Poisson',mean(dl)),x);

>> [h,p]=chi2gof(x,'Ctrs', x, 'Frequency', ts, 'Expected',tslt, 'NParams', 1)

the results are: h = 0 p = 0.1019

3. >> [h,p]=kstest(dl','CDF', makedist('Poisson',mean(dl)))

h =1 p = 7.8989e-08

3 ways return 3 different results. Please help me explain why it is

Answer 1

[Torsten]

"kstest" is not applicable since the Poisson Distribution is a discrete, not a continuous distribution.

Since the example "Test for Poisson Distribution" under

https://uk.mathworks.com/help/stats/chi2gof.html

shows you how to proceed, I'd go this way.

bins = 0:3;
obsCounts = [7 18 11 4];
n = sum(obsCounts);
pd = fitdist(bins','Poisson','Frequency',obsCounts');
expCounts = n * pdf(pd,bins);
[h,p,st] = chi2gof(bins,'Ctrs',bins,...
                        'Frequency',obsCounts, ...
                        'Expected',expCounts,...
                        'NParams',1,...
                        'Alpha',0.05)

h = 0

p = 0.1019

st = struct with fields:
    chi2stat: 2.6749
          df: 1
       edges: [-0.5000 0.5000 1.5000 3.5000]
           O: [7 18 15]
           E: [10.9013 14.1717 13.2033]

[Dan]

thank for your help!