Modeling proportion of success in high school leaving certificate examination-a comparative study of inflated unit Lindley and inflated beta distribution

Abstract

In this article, we first introduced the inflated unit Lindley distribution considering zero or/and one inflation scenario and studied its basic distributional and structural properties. Both the proposed distributions are shown to be members of exponential family with full rank. Different parameter estimation methods are discussed along with supporting simulation studies to check their efficacy. Proportion of students passing the high school leaving certificate examination for the schools across the state of Manipur in India for the year 2020 are then modeled using the proposed distributions and compared with the inflated beta distribution to justify its benefits.