Cubic Transmuted Lindley as a Better Distribution in the Family of Rayleigh Distributions

Abstract

A new statistical model for non-normal data is proposed with some of its statistical properties as Cubic of the Transmuted Lindley distribution (CTLD), based on a new family of life time distribution. The new model contains some of lifetime distributions as special cases such as exponentiated Lindley, transmuted Lindley and Lindley distributions. These include the density and hazard rate functions with their behavior, moments, and moment generating function, skewness and kurtosis measures. Maximum likelihood estimation of the parameters and their estimated are derived. An application of the model to a real data set is presented and compared with the fit attained by other well-known existing distributions.