  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.
