Application of multi criteria method to identify the best-fit statistical distribution

Abstract

Generally, researchers are faced to identify the true statistical distributions for the analysis of a various hydrologic data sets. Using traditional statistical analysis methods one choose a hypothesized distribution to describe the observed data, estimate the distribution parameters and then apply the goodness of fit test such as the Chi Square test (CS) or Kolmogorov Smirnov (KS) test. For more accurate, several factors or criteria should be considered in selection of the best distribution. However when more than two criteria are used to identify the best distribution, it is more difficult and more subjective. In this paper, we propose a new Multi Criteria Decision Making method (MCDM) based on nonlinear programming for selection of the best distribution to fit a set of data. The Generalized Extreme Value (GEV), Generalized Pareto (GP), Pearson 3 (P3) and Lognormal 3 (LN3) are used and their goodness of fit has been examined by various test statistics. A numerical example is used to illustrate the applicability of the proposed approach.