2019/09/27 by Abhik Ghosh, Ghosh, Abhik, Preety Shreya +3
Physics and Astronomy · Environmental Science · Economics, Econometrics and Finance · #Statistical Mechanics and Entropy #Hydrology and Drought Analysis #Complex Systems and Time Series Analysis
paper · pdf · doi:10.48550/arxiv.1909.12542
In this paper we derive the maximum entropy characteristics of a particular\nrank order distribution, namely the discrete generalized beta distribution,\nwhich has recently been observed to be extremely useful in modelling many\nseveral rank-size distributions from different context in Arts and Sciences, as\na two-parameter generalization of Zipf's law. Although it has been seen to\nprovide excellent fits for several real world empirical datasets, the\nunderlying theory responsible for the success of this particular rank order\ndistribution is not explored properly. Here we, for the first time, provide its\ngenerating process which describes it as a natural maximum entropy distribution\nunder an appropriate bivariate utility constraint. Further, considering the\nsimilarity of the proposed utility function with the usual logarithmic utility\nfunction from economic literature, we have also explored its acceptability in\nuniversal modeling of different types of socio-economic factors within a\ncountry as well as across the countries. The values of distributional\nparameters estimated through a rigorous statistical estimation method, along\nwith the entropy values, are used to characterize the distributions of all\nthese socio-economic factors over the years.\n