A comparison study on a new five-parameter generalized Lindley distribution with its sub-models - Tharshan, R.; Wijekoon, P. (Polish Statistical Association, 2020)
In recent years, modifications of the classical Lindley distribution have been considered by many authors. In this paper, we introduce a new generalization of the Lindley distribution based on a mixture of exponential and gamma distributions with different mixing propor tions and compare its performance with its sub-models. The new distribution accommodates the classical Lindley, Quasi Lindley, Two-parameter Lindley, Shanker, Lindley distribution with location parameter, and Three-parameter Lindley distributions as special cases. Various structural properties of the new distribution are discussed and the size-biased and the length biased are derived. A simulation study is conducted to examine the mean square error for the parameters by means of the method of maximum likelihood. Finally, simulation studies and some real-world data sets are used to illustrate its flexibility in terms of its location, scale and shape parameters.
Keywords: Lindley distribution; Mixture distributions; Size-biased distributions; maximum likelihood estimation