On an Inflated Unit-Lindley Distribution

TL;DR

This paper introduces an inflated unit-Lindley distribution for modeling fractional data on [0,1], addressing inflation at both ends, and compares its performance with existing distributions through simulations and real data analysis.

Contribution

The paper proposes a new inflated unit-Lindley distribution with properties and estimation methods, and evaluates its effectiveness against existing models.

Findings

The inflated unit-Lindley distribution fits fractional data well.

It outperforms some existing models in simulations.

Real-data analysis confirms its practical usefulness.

Abstract

Modeling fractional data in various real life scenarios is a challenging task. This paper consider situations where fractional data is observed on the interval [0,1]. The unit-Lindley distribution has been discussed in the literature where its support lies between 0 and 1. In this paper, we focus on an inflated variant of the unit-Lindley distribution, where the inflation occurs at both 0 and 1. Various properties of the inflated unit-Lindley distribution are discussed and examined, including point estimation based on the maximum likelihood method and interval estimation. Finally, extensive Monte Carlo simulation and real-data analyses are carried out to compare the fit of our proposed distribution along with some of the existing ones such as the inflated beta and the inflated Kumaraswamy distributions.