Dear Researchers,
I am using ARENA Input Analyzer to get the best probability distribution from data (attached). The resulted p-value of Chi Square Test < 0.005 and for K-S Test > 0.15. Should I accept the resulted probability distribution regardless of Chi Square Test p-value?
Dear Mahmoud,
From your output there seems to be something wrong with the number of intervals for your chi-square test - perhaps this needs to be redone. The histogram data does seem to fit the curve quite nicely so I would suspect the K-S result is more accurate.
Another thought: I don't know whether it is possible but it might be more accurate to use intervals with approximately equal frequencies rather than equal values of the independent variable.
Mahmoud -
I see "degrees of freedom = -1." What could that mean???
At any rate, looking at your histogram, it appears that you do not have enough data to too clearly depict distribution parameters in this case, other than to say that it must be a highly skewed distribution.
By the way, p-values are often misleading anyway, and never give 'the whole story.'
Cheers - Jim
PS - Ah. I see that Peter asked about the number of intervals for the chi-square "test," which gave you the -1 df, I suppose, but I am not sure how.
PSS - Actually, I see that you have n = 111, so that may be enough data to show you more about your distribution if you just did a histogram from the first two or three bins near the origin, however many observations are there, and subdivided that for such a new histogram. Trying different bin sizes for that group might be enlightening.
The KS test uses the maximum deviation for the evaluation, whereas the chi-squared test uses the mean deviation between the data and the model. Usually, the KS test is more demanding than the chi-squared. In your experiment, both test display low p values, which indicates the similarity between data and model is not good.
By looking at the picture you provide I notice that the bins of the histogram are too wide. Also, there are few bins. You should consider gathering more data for suppressing regions with no bins and taking more precise measurements which will make bins narrower. This will help you improving the fit, and performing a better evaluation of the samples.
Summarizing, I think you should not accept the resulted probability distribution.
The following papers may be useful to your research
Good Luck!
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