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 bathtubshaped. 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.

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This paper is devoted to a new lifetime distribution having three parameters by compound the exponential model and the transmuted Topp-Leone-G. The new proposed model is called the transmuted Topp-Leone exponential model; it is useful in lifetime data and reliability. The new model is very flexible; its pdf can be right skewness, unimodal, and decreasing shaped, but the hrf of the suggested model can be unimodal, constant, and decreasing. Numerous statistical characteristics of the new model, notably the quantile function, moments, incomplete moments, conditional moments, mean residual life, mean inactivity time, and entropy are produced and investigated. The system’s parameters are estimated using the maximum likelihood approach. All estimators should be theoretically convergent, which is supported by a simulation analysis. Finally, two real-world datasets from the engineering and medical disciplines explore the new model’s relevance and adaptability in comparison to the alternatives models such as the beta exponential, the Marshall–Olkin generalized exponential, the exponentiated Weibull, the modified Weibull, and the transmuted Burr type X models.