A new method for constructing continuous distributions on the unit interval

TL;DR

This paper introduces a novel method for constructing continuous distributions on the unit interval by conditioning on the convolution of two positive random variables, leading to new distribution structures and improved modeling capabilities.

Contribution

The paper presents a new convolution-based approach for creating continuous distributions on [0,1], including formulations of existing distributions and new structures with practical applications.

Findings

New distribution structures with potential for real-world applications

Demonstrated improved fit over existing models in a case study

Method applicable to various positive distributions like exponential and gamma

Abstract

A novel approach towards construction of absolutely continuous distributions over the unit interval is proposed. Considering two absolutely continuous random variables with positive support, this method conditions on their convolution to generate a new random variable in the unit interval. This approach is demonstrated using some popular choices of the positive random variables such as the exponential, Lindley, gamma. Some existing distributions like the uniform and the beta are formulated with this method. Several new structures of density functions having potential for future application in real life problems are also provided. One of the new distributions having one parameter is considered for parameter estimation and real life modelling application and shown to provide better fit than the popular one parameter Topp-Leone model.