There are various goodness of fit test available such as Kolmogorov Smirnov Test, Anderson Darling Test, Chi-Squared Test etc. These tests are used to rank the probability distributions, but when we see the results, it can be observed that different tests give different rank to the probability distribution and most of the cases huge difference can be seen. So, my question is how can we know that which goodness of fit test should we consider for a dataset. Is there any criteria for choosing such test
Dear Tapasranjan Das
Kolmogorov Smirnov test is considered to be good test. And the statisticians depending on the most best one for all Tests. That is mean the first rank distribution in most test is the best choose
Robert A Canales Thank you for your valuable information. In my case I am more interested in assessment of extremes alongwith return period(say 2,5,10,25,50 and 100 year return period) of the values. So my area of interest starts from probability of occurrence greater than 0.5 in the cdf of the distribution. Will the Anderson-Darling Test be sufficient for testing the goodness of fit?
Abbas Lafta Kneehr Thank you so much for your valuable information. Could you please suggest me some reference material so that I can justify my point on considering a particular goodness of fit test.
The chi-square, the Kolmogorov-Smirnov test(K-S), the Anderson-Darling test(A-D), Cramér-von Mises test(C-S) and the Shipiro-Wilk test(S-W) are amongst the most common Goodness-of-fit test methods used in statistics. As compared to an absolute measure of how a particular distribution fits the data, the K-S, C-S, and A-D test statistics values are used to compare the fit of competing distributions(usually continuous distributions). Smaller statistical values for the K-S, C-S, and A-D tests suggest that the distribution fits the data better.
However, the Anderson-Darling test is used to determine whether a sample of data originated from a population with a specific distribution. This is a variation of the Kolmogorov-Smirnov (K-S) test and gives the tails greater weight than the K-S test does.
I hope this is helpful.
Robert A Canales Thank you again for the help. The material you referred to is of great help.
Dear Das
You can download esayfit software which is used to test many testing and choice the best one
http://www.mathwave.com/easyfit-distribution-fitting.html.
You may wish to check the value produced by each of the goodness of fit statistics and hence their p values. Since each statistic attempts to measure the discrepancies between the observed and the expected, the closer these values are the smaller the value of test Statistics will be and also the closer the p value to 1. Thus, a test Statistic with smallest value which is likely going to be associated with p value closest to 1 may be preferred. In another perspective, one can use the goodness of fit measures ( any of AIC, BIC...) to make a choice. The one that gives smallest value is best.
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