A new generalized Lindley distribution, based on weighted mixture of two gamma distributions, is proposed. This model includes the Lindley, gamma and exponential distributions as and other forms of Lindley distributions as special cases. Lindley distribution based on two gamma with two consecutive shape parameter is investigated in some details. Statistical and reliability properties of this model are derived. The size-biased, the length-biased and Lorenze curve are established. Estimation of the underlying parameters via the moment method and maximum likelihood has been investigated and their values are simulated. Finally, fitting this model to a set of real-life data is discussed.

In this paper, we introduce a new distribution generated by an integral transform of the probability density function of the weighted exponential distribution. This distribution is called the weighted exponential-Gompertz (WE-G). Its hazard rate function can be increasing and bathtub-shaped. Several statistical properties of the new model are obtained, such as moment generating function, moments, conditional moments, mean inactivity time, mean residual lifetime and Rényi entropy. The maximum likelihood estimation of unknown parameters is introduced. A real data application demonstrates the performance of the new model.

Accurately modeling heavy-tailed data is critical across applied sciences, particularly in finance, medicine, and actuarial analysis. This work presents the heavy-tailed power XLindley distribution (HTPXLD), a unique heavy-ta... | Find, read and cite all the research you need on Tech Science Press