Modeling proportion of success in high school leaving examination- A comparative study of Inflated Unit Lindley and Inflated Beta distribution

TL;DR

This paper introduces the inflated unit Lindley distribution, explores its properties, and compares its effectiveness with the inflated beta distribution in modeling high school exam success rates in Manipur, India.

Contribution

It proposes a new inflated unit Lindley distribution, analyzes its properties, and demonstrates its advantages over the inflated beta distribution for modeling exam success proportions.

Findings

The inflated unit Lindley distribution effectively models exam success proportions.

Simulation studies confirm the estimation methods' efficacy.

The proposed distribution outperforms the inflated beta in certain scenarios.

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 distributions are shown to be members of exponential family with full rank. Different parameter estimation methods are discussed and supporting simulation studies to check their efficacy are also presented. Proportion of students passing the high school leaving 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.