Probability distribution selection using PROMETHEE GDSS method

Abstract

Rising inequalities between countries are widely investigated. Since they involve different aspects, in this paper they are examined through the distribution of countries’ growth and development, inclusion and intergenerational equity and sustainability. These aspects involve variables that are not normally distributed so different probability density functions (PDFs) have been proposed, tested and compared through literature. This paper compares different PDFs that are considered successful in describing distribution of the variables involved, as Weibull, gamma, lognormal, normal, loglogistic, Pareto, Burr and exponential. They are usually compared using diff erent goodness-of-fit measures including the log-likelihood, sum of squared errors, sum of absolute errors and chi-square statistics which can sometimes lead to divergent conclusions. This paper adds up to these goodness-of-fit measures and includes the Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling statistics, the mean absolute and squared deviation between theoretical and empirical PDF, the mean absolute and squared deviation between theoretical and empirical cumulative distribution function, AIC and BIC as well as the deviation in skewness and kurtosis. Since diff erent distributions can be considered as alternatives and goodness-of-fit measures as conflicting criteria, the problem of finding the appropriate PDF can be viewed as multiple criteria decision making problem which can be solved using PROMETHEE method. However, diff erent preference parameters, lead to different ranking, so the final decision is obtained using PROMETHEE Group Decision Support System (GDSS) method. This paper therefore contributes to the existing literature on inequalities between countries and statistics in general by proposing a new approach for distribution modelling and selection.