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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
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.

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Answers (1)

Jeff Miller
Jeff Miller on 18 Mar 2020
kstest does return a p value as the second output. Maybe you are supposed to report that.


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