New class of Lindley distributions: properties and applications

Duha Hamed,Ahmad Alzaghal

doi:10.1186/s40488-021-00127-y

Abstract

A new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

Highlights

Introduction and motivation TheLindley distribution was first introduced as a one scale parameter distribution by Lindley (1958)
Another two-parameter Lindley distribution was introduced by Dey et al (2019), which provides a better fit to skewed real data than the inverse Lindley distribution introduced by Sharma et al (2015)
Using Eq (1) with FR(x) to be the cumulative distribution function (CDF) defined in Eq (3), the CDF and probability density function (PDF) of the random variable X following the general T-Lindley{Y } class of distributions are, respectively, given as θx θ +1 e−θ x fT (t)dt = FT

Summary

Introduction

Introduction and motivation TheLindley distribution was first introduced as a one scale parameter distribution by Lindley (1958). 0. Using Eq (1) with FR(x) to be the CDF defined in Eq (3), the CDF and PDF of the random variable X following the general T-Lindley{Y } class of distributions are, respectively, given as θx θ +1 e−θ x fT (t)dt = FT

Results

Conclusion