Ten Ways to Specify a Gini Coefficient Using Entropy

Our friend and frequent collaborator Prof. Michael McAleer loved to enumerate lists and to give practical advice. Here, we present a review of 10 ways to derive the well-known Gini coefficient based on entropy measures. In fact, Mike was a collaborator on some of this work, as will be discussed in the paper. All are useful ways to combine two powerful tools, entropy measures and Gini coefficients to examine inequality in income distribution functions (IDFs) and can be applied to distributions of other random variables. Others have shown that a Gini coefficient can be derived from the first moment of an observed share function. Ryu and Slottje demonstrated that by projecting the observed share function with other moments and functions different approximated share functions can be derived. By doing so, more information can be conveyed about the underlying IDF that generated the observed Gini value. In the spirit of Prof. Michael McAleer, we present 10 different ways to utilize entropy functions to generate Gini coefficient measures.