Density Sharpening: Principles and Applications to Discrete Data Analysis

TL;DR

This paper introduces Density Sharpening, a new statistical modeling principle for discrete data that unifies various methods through nonparametric approximation and smoothing, demonstrated across diverse real-world applications.

Contribution

It presents a novel theory of nonparametric approximation for discrete distributions and applies it to develop the Density Sharpening framework, unifying existing methods.

Findings

Effective modeling of discrete count data using Density Sharpening

Successful applications in seismology, healthcare, and physics

Provides a theoretical foundation for discrete distribution smoothing

Abstract

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.