Abstract In this paper, a new three-parameter lifetime model called the Topp–Leone odd log-logistic exponential distribution is proposed. Its density function can be expressed as a linear mixture of exponentiated exponential densities and can be reversed-J shaped, skewed to the left and to the right. Further, the hazard rate function of the new model can be monotone, unimodal, constant, J-shaped, constant-increasing-decreasing and decreasing-increasing-decreasing and bathtub-shaped. Our main focus is on estimation from a frequentist point of view, yet, some statistical and reliability characteristics for the proposed model are derived. We briefly describe different estimators namely, the maximum likelihood estimators, ordinary least-squares estimators, weighted least-squares estimators, percentile estimators, maximum product of spacings estimators, Cramér-von-Mises minimum distance estimators, Anderson-Darling estimators and right-tail Anderson-Darling estimators. Monte Carlo simulations are performed to compare the performance of the proposed methods of estimation for both small and large samples. We illustrate the performance of the proposed distribution by means of two real data sets and both the data sets show the new distribution is more appropriate as compared to some other well-known distributions.
Abstract: We introduce a new class of continuous distributions called the generalized odd Lindley-G family. Four special models of the new family are provided. Some explicit expressions for the quantile and generating functions, ordinary and incomplete moments, order statistics and Rényi and Shannon entropies are derived. The maximum likelihood method is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.
Abstract We introduce a new three-parameter lifetime model called the Lindley Weibull distribution, which accommodates unimodal and bathtub, and a broad variety of monotone failure rates. We provide a comprehensive account of some of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear combination of exponentiated Weibull densities. The maximum likelihood method is used to estimate the model parameters. We present simulation results to assess the performance of the maximum likelihood estimation. We prove empirically the importance and flexibility of the new distribution in modeling two data sets.