A NEW FAMILY OF LINDLEY DISTRIBUTIONS FEATURING BIMODAL CASES

Several lifetime distributions have been developed in literature to handle different real-world scenario. Most of these distributions were developed to model a unimodal (symmetric or asymmetric) data. Only a hand-full of these distributions exhibits a bimodal property. This paper explores a new family of Lindley distributions featuring a bimodal property. We introduce five different sub-families of the T-Power Lindley{Y} family based on the quantile function of the uniform, exponential, Frechet, log-logistic and logistic distributions. Useful mathematical properties of the proposed T-Power Lindley{Y} family of distributions are derived and sub-models were the random variable T follows the one-parameter ToppLeone, exponential, exponentiated exponential, Weibull and Gumbel distributions are introduced. From the graphical representation of the density function of these sub-models, we observe that the shape of the density function accommodates a decreasing (reversed-J), left-skewed, right-skewed, symmetric, as well as a bimodal shape. In order to illustrate the usefulness and performance of the proposed T-Power Lindley{Y} family of distributions, the Gumbel Power Lindley (GPL) distribution belonging to the proposed family of distribution was employed to fit a bimodal data set alongside with the beta-Normal distribution. Result obtained from the analysis revealed that the Gumbel Power Lindley (GPL) distribution compares favourably better than the beta-Normal distribution. The density fits of the distributions for the data set was also investigated to support the claim.