Test for Poisson distribution

I have a vector of observations (length: 1195).

Previous studies have found the data to have a Poisson distribution, and when I plot the data it closely resembles what I would expect to see from a Poisson distribution (see image below).

And the fit (and quality metrics) looks like the following,

Distribution: Poisson

Log likelihood: -5094.64

Domain: 0 <= y < Inf

Mean: 5.63264

Variance: 5.63264

Parameter Estimate Std. Err.

lambda 5.63264 0.068655

Estimated covariance of parameter estimates:

lambda

lambda 0.0047135

However, when I test the hypothesis using a Cho-squared goodness of fit test (chi2gof) as detailed here, Chi-square goodness-of-fit test - MATLAB chi2gof - MathWorks Nordic, the results indicate that the hypothesis should be rejected (at alpha 0.05).

I am not confident I have not made a mistake, and would really appreciate some input. The following is the code for the chi2gof test,

n = sum(x);
bins = 0:1194;
pd = fitdist(bins','Poisson','Frequency',x');
expCounts = n * pdf(pd,bins);
[h,p,st] = chi2gof(bins,'Ctrs',bins,...
'Frequency',x, ...
'Expected',expCounts,...
'NParams',1)

Here is a sample of x (1:100),

x = [3,1,3,4,0,0,0,4,10,2,0,4,6,2,2,2,5,2,0,4,4,2,1,2,3,3,6,0,3,2,0,0,2,4,4,3,0,0,2,3,0,0,0,0,0,0,0,0,1,1,3,2,2,2,1,8,2,4,6,0,3,1,3,1,3,1,1,4,1,2,9,6,6,0,11,3,0,1,2,2,3,0,6,0,3,0,8,5,8,6,7,5,5,0,8,1,3,0,0,8]

Answer 1

[Abdolkarim Mohammadi]

Maybe the problem is that you have created too many bins; one bin for each observation. That would not yield good results. Consider lowering the number of bins.

In addition, x is your data and NOT the frequency. You can use the histcounts() function to get the desired bins.