# P-value of a fitted distribution to observation?

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frankovaT on 17 Mar 2020
Commented: Adam Danz on 21 Mar 2020
I have an observation data set (of 300 observations). I fitted 5 different distribution on this data. I wish to check which distribution fits best to this observation. apart from using some goodness of fit measures (such as Root mean square or kolmograv-smirnov), i got to report the p value of my fitted distributions as well.
I dont understand this quite well. what does it mean to report a P value here? should i have different P value s for different goodness of fit measures, or should I have it between observation and distribution-based values? how should I calculate this mathematically?
I dont want a built in code in matlab, I want to know how it is done mathematically? should I sample from the data?
how big must the sample be? or is there any other procedure ? stat

Adam Danz on 18 Mar 2020
"what does it mean to report a P value here?"
That's the correct question to be asking. A p-value returns the probability of getting the results of some test given that the null hypothesis is correct. If the p value is low enough, you reject the null hypothesis.
If you have 5 different distributions all with different fit values, what's the null hypothesis about those 5 values? When the question is framed that way, it's clear that this isn't the right question to ask.
The One-sample Kolmogorov-Smirnov test returns a test decision (output 1) for the null hypothesis that the input data comes from a standard normal distribution, against the alternative that it does not come from such a distribution. The p-value (output 2) is the probability value used to make the test decision.
Lastly, the confusion over p-values is common which has motivated hundreds of statisticians and researchers across the globe to deemphasize the use of p-values in statistical reporting (Nature, March 2019).
frankovaT on 18 Mar 2020
Dear Adam, Thanks for your comment, actually it hepled me through my ocnfusion.
Adam Danz on 21 Mar 2020
Thanks for the feedback!