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.

在本文中，我们为两参数秩序（RO）分布（即离散广义beta分布（DGBD））制定了一个最大熵框架，最近发现该模型在建模来自艺术与科学的不同背景，作为Zipf定律的两参数推广。尽管已经发现它可以很好地拟合几个实际的经验数据集，但是对于这种特定等级顺序分布的成功负责的基本理论却没有得到适当的探讨。在这里，我们第一次提供其生成过程，将其描述为在适当的双变量效用约束下的自然最大熵分布。此外，我们已经表明，通过RO分布从适当的约束条件估计概率模型中使用的最大熵原理也是许多社会经济模型的基础。我们已经证明了在模拟一个国家内以及整个国家不同类型的社会经济因素时的可接受性。$ËñŤ\mathrm{[R}Øpÿ$ 这些值用于表征这些年来所有这些社会经济因素的分布。