A family of discrete maximum-entropy distributions

Abstract

In this paper, a family of maximum-entropy distributions with general discrete support is derived. Members of the family are distinguished by the number of specified non-central moments. In addition, a subfamily of discrete symmetric distributions is defined. Attention is paid to maximum likelihood estimation of the parameters of any member of the general family. It is shown that the parameters of any special case with infinite support can be estimated using a conditional distribution given a finite subset of the total support. In an empirical data example, the procedures proposed are demonstrated.