Maximum entropy framework for a universal rank order distribution with socio-economic applications

Abstract

In this paper, we formulate a maximum entropy framework for a two-parameter Rank-Order (RO) distribution, namely the discrete generalized beta distribution (DGBD), which has recently been observed to be extremely useful in modeling several rank-size distributions from different context in Arts and Sciences, as a two-parameter generalization of Zipf’s law. Although it has been seen to provide excellent fits for several real world empirical datasets, the underlying theory responsible for the success of this particular rank order distribution is not explored properly. Here we, for the first time, provide its generating process which describes it as a natural maximum entropy distribution under an appropriate bivariate utility constraint. Further, we have shown that the maximum entropy principle used in estimating probabilistic models from appropriate constraints, via the RO distribution, is also the underlying basis of many socio-economic models. We have demonstrated its acceptability in modeling of different types of socio-economic factors within a country as well as across the countries. The values of distributional parameters estimated through a rigorous statistical estimation method, along with the entropy values, are used to characterize the distributions of all these socio-economic factors over the years.