I have prepared an analysis of time series extreme values data sets (9 sets for different storm durations) by using three PDFs i.e. General Extreme Value (GEV), LogPearson III (LP III), and Gumbel Max (EV), then I applied three GOF tests ( Kolmogorov–Smirnov (K-S), Anderson–Darling (A-D) and chi-squared test (χ2)) to select the best PDF. Results show that the thee PDFs accepted at alpha = 5% for the 9 cases. The ranking of the PDFs for each data set is given in the attached table. Based on these results, the GEV is ranked as 1st in 7 out of 9 cases. Can I take my decision that the GEV is the best one or there is another method to conclude the best one according to the ranking result?
Thanks in advance for your answers.
In supplement to the three classical GOF statistics you already conducted, depending on your discretion, you can also consider examining the quality of fit using empirical and theoretical distributions, cumulative density function, P-P and Q–Q plots.
Subsequent to conducting the maximum likelihood estimation (MLE) and goodness-of-fit (GOF) tests, the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) values must in standard practice be calculated for use to identify the best-fit distribution. Thereafter, the best-fit distribution is then selected based on the minimum or lowest AIC and BIC values computed.
Overall, the best-fit distribution is the one that best meets the criterion of both the goodness-of-fit statistics and information criteria-based model selection for the extreme (maximum and minimum) datasets.
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