Density Sharpening: Principles and Applications to Discrete Data Analysis

This article introduces a general statistical modeling principle called ``Density Sharpening'' and applies it to the analysis of discrete count data. The underlying foundation is based on a new theory of nonparametric approximation and smoothing methods for discrete distributions which play a useful role in explaining and uniting a large class of applied statistical methods. The proposed modeling framework is illustrated using several real applications, from seismology to healthcare to physics.