A New Unit Generated Family of Distributions: Classical Estimation Methods and Applications to Real Data

Abstract

In this article, a new unit-generated family of distributions called the unit inverse Lindley family is investigated and discussed. Four sub-models of the suggested truncated family are discussed, such as unit inverse Lindley- exponential, unit inverse Lindley- Lomax, unit inverse Lindley- Topp Leone, and unit inverse Lindley- Kumaraswamy distributions. Some important Statistical features of the new unit-generated family are computed, such as quantiles, moments, and moment generating function. Different types of entropies, such as R\'{e}nyi entropy, Tsallis entropy, Havrda and Charvat entropy, and Arimoto entropy, are computed. Sixteen different approaches of estimation, such as maximum likelihood, least-square, a maximum product of spacing, weighted least square, Cramér-von Mises, and Anderson--Darling, are discussed to estimate the parameters. Monte Carlo simulations are used to investigate the performance of the estimation methodologies. In the end, two real-world datasets are examined to show the practical applicability and relevance of the suggested family.