  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.
