Inflated Beta Distributions

TL;DR

This paper introduces mixed continuous-discrete distributions using the beta distribution to model fractional data within [0,1], exploring their properties, estimation methods, and practical applications.

Contribution

It proposes a novel mixed distribution framework for fractional data using beta distributions, with analysis of properties and estimation techniques.

Findings

Properties of the proposed distributions are thoroughly examined.

Maximum likelihood and method of moments estimations are discussed.

Real data applications demonstrate the models' practical usefulness.

Abstract

This paper considers the issue of modeling fractional data observed in the interval [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model since its density can have quite diferent shapes depending on the values of the two parameters that index the distribution. Properties of the proposed distributions are examined. Also, maximum likelihood and method of moments estimation is discussed. Finally, practical applications that employ real data are presented.