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I have a data set and I would like to fit a t distribution on it. I use R or Python to feed into my data, and I get the degrees of freedom, the location and the scale parameters.

After that, I generated random t distributed numbers with the parameters I got from my data set. Then I compared these random numbers with the original data using the Kolmogorov Smirnov and the Anderson-Darling tests. Both rejected the Null hypothesis.

I would like to know why this happens and what could I do about it?

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    $\begingroup$ Does it happen with any sample you generate or only sometimes? How often it does happen? $\endgroup$ – Aksakal Oct 5 '18 at 14:06
  • $\begingroup$ It happens with every sample. $\endgroup$ – Alquil Oct 5 '18 at 14:11
  • $\begingroup$ You might try my online open source Python statistical distribution fitter and see if it can suggest a scipy continuous distribution to consider, the link is zunzun.com/StatisticalDistributions/1 with source code links at the bottom of the web page. $\endgroup$ – James Phillips Oct 5 '18 at 18:41
  • $\begingroup$ How large is the sample? $\endgroup$ – SecretAgentMan Oct 8 '18 at 1:47
  • $\begingroup$ @SecretAgentMan It has almost 2000 observations $\endgroup$ – Alquil Oct 8 '18 at 7:19
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This seems to suggest that your original data is not, in fact, t-distributed. You could fit a t-distribution to literally any data set, that doesn't mean it will describe your data well. The fact that your tests reject the null hypothesis shows that there is a mismatch between the distribution of your data and your fitted t-distributed samples.

Maybe try to fit a different distribution to your data, since it is significantly different from t-distributed.

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