A multi-criterion evaluation approach to selection of the best statistical distribution

Using traditional statistical analysis methods one chooses a hypothesized distribution to describe the observed data, estimate the distribution parameters, and then apply the Kolmogorov-Smirnov test statistic Dmax or the Chi-square test statistic χ2 to test the goodness of fit. Observing that the Dmax statistic considers only the information on cumulative distribution function (CDF), we have proposed a multi-criterion decision-making approach considering not only the Dmax statistic but also the errors in CDF, the errors in probability distribution function, the errors in skewness and kurtosis, and expertsʹ preference. A case study is provided to illustrate the use of the proposed approach.