A New Gamma Generalized Lindley-Loglogistic Distribution with Applications

Abstract

A new distribution called the gamma exponentiated Lindley Log-logistic (GELLLoG) distribution is developed. Some properties of the new distribution including hazard function, quantile function, moments, conditional moments, mean and median deviations, Bonferroni and Lorenz curves, distribution of the order statistics and Renyi entropy are derived. Maximum likelihood estimation technique ´ is used to estimate the model parameters. We conduct a simulation study to examine the bias and mean square error of the maximum likelihood estimators. Finally, applications to real datasets to illustrate the usefulness of the proposed distribution are presented.

Key words: Gamma distribution; Lindley distributions: Exponentiated distribution: Long-logistic distribution: Generalized distribution: Maximum likelihood estimation