Generalized quasi Lindley distribution: theoretical properties, estimation methods and applications

In this paper, a new continuous two parameters generalized quasi Lindley distribution (GQLD) is suggested. The GQLD is a sum of two independent quasi Lindley distributed random variables. Comprehensive statistical properties of the new model are provided in closed forms includes moments, reliability function, hazard function, reversed hazard function, stochastic ordering, stress-strength reliability, and distribution of order statistics. The unknown parameters of the new distribution are estimated by the maximum likelihood, maximum product of spacing, ordinary least squares, weighted least squares, Cramer-von-Mises, and Anderson-Darling methods. A detailed simulation study is conducted to investigate the efficiency of the proposed estimators in terms of mean square errors. The performance of the suggested model is illustrated using two real data sets. It turns out that the GQLD can provide better fits than the quasi Lindley, Pareto, two-parameter Sujatha, and log-normal distributions.

Automated summary

In this paper, a new continuous two parameters generalized quasi Lindley distribution (GQLD) is suggested. The comprehensive statistical properties and parameter estimation methods of the GQLD are provided. The simulation study and data analysis results demonstrate that the GQLD can provide better fits than other distributions.