The Gompertz Weibull Frechet Distribution: ´ Properties and Applications

  • Winai Bodhisuwan Department of Statistics, Kasetsart University, Bangkok, Thailand
  • Sirinapa Aryuyuen Department of Mathematics and Computer Science, Rajamangala University of Technology Thanyaburi, Pathum Thani, Thailand
Keywords: Weibull Frechet distribution, Gompertz-G family of distributions, maximum likelihood ´ estimation, hazard function, stochastic ordering


A new distribution namely the Gompertz-Weibull Frechet (Go-WFr) distribution is proposed. It ´is a class of Gompertz-G family of distributions. Some statistical properties of the proposed distribution including the reliability function, hazard function, quantile function, moments, and Lorenz and Bonferroni curves are discussed. The proposed distribution has five sub-models, that is, Gompertzexponential Frechet, Gompertz-Weibull inverse exponential, Gompertz-Weibull inverse Rayleigh, ´Gompertz-exponential inverse exponential, and Gompertz-exponential inverse Rayleigh distributions. The parameters of the Go-WFr are estimated by using the maximum likelihood estimation. Simulation studies and the application of the proposed distribution are illustrated.


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