Abstract
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.
Highlights
Numerous extended distributions have been extensively used over the last decades for modelling data in several areas
We provide a new family of distributions generated by the weighted exponential distribution
We introduce a new family of distributions generated by an integral transform of the pdf of a random variable T which follows weighted exponential (WE) distribution
Summary
Numerous extended distributions have been extensively used over the last decades for modelling data in several areas. Zografos and Balakrishnan [2] have presented a new family of distributions generated by a gamma random variable We introduce a new family of distributions generated by an integral transform of the pdf of a random variable T which follows WE distribution. Motivation 4: Substituting α = 1 in Equation (7), we obtained the pdf of the generalized transmuted-G family with parameters (λ = 1, a = b = β) proposed by Nofal et al [6] as f (x) = 2 β g(x; ζ ) Gβ−1(x; ζ )(1 − Gβ (x; ζ )). We study the properties of a special case of this family, when G(·) is the cdf of the Gompertz distribution In this case, the random variable X is said to have the weighted exponential-Gompertz distribution.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
