Statistical Inference Of The Exponentiated Gamma Distribution

Since Gupta et al.put forward the exponentiated gamma model in 1998,its superior performance in life data fitting has attracted the attention of many scholars.In order to improve the theoretical study of exponentiated gamma distribution,this paper studies the parameter estimation of exponentiated gamma distribution based on life test,accelerated life test and stress strength model.Firstly,assume that the failure data in the life test follow the exponentiated gamma distribution,the inverse moment estimation and generalized interval estimation of the model parameters and reliability index are given.In terms of point estimation,the absolute error and mean square error of the inverse moment estimation and maximum likelihood estimation are compared by numerical simulation.The results show that the inverse moment estimation has better effect.In terms of interval estimation,the interval coverage and average interval length of generalized confidence interval,Wald confidence interval and Bootstrap confidence interval are compared by numerical simulation.The results show that the performance of generalized confidence interval estimation is better than Wald and Bootstrap confidence interval estimation.Moreover,the generalized interval estimation has a good effect on the estimation of average life,reliability and 0.1 quantile.Secondly,the inverse moment estimation and generalized interval estimation of the model parameters are given under the assumption that the failure data under each accelerating stress in the constant additive life test follow the exponentiated gamma distribution.In terms of point estimation,the absolute error and mean square error of the inverse moment estimation and maximum likelihood estimation are compared by numerical simulation,and the results show that the inverse moment estimation is better.In terms of interval estimation,the interval coverage and average interval length of generalized confidence interval,Wald confidence interval and Bootstrap confidence interval are compared by numerical simulation.The results show that the performance of generalized confidence interval estimation is generally better than Wald and Bootstrap confidence interval estimation.Finally,in the stress strength model,it is assumed that the stress variables X and strength variables Y are independent of each other and obey the exponentiated gamma distribution with parameters(λ1,θ1)and(λ2,θ2),respectively.The point estimation and interval estimation of the reliability in the model are discussed in three cases:λ1=λ2=λ,θ1=θ2=θ and λ1≠λ2,θ1≠θ2,respectively.For point estimation,the inverse moment estimation method and maximum likelihood estimation method are used,and for interval estimation,generalized interval estimation method and Bootstrap interval estimation method are used.Numerical simulation results show that the inverse moment estimation and generalized interval estimation have better performance in general under the three conditions.