Inference For The Generalized Inverted Exponential Distribution Under Progressive First Failure Censoring

With the development and improvement of technology,the life of product tends to be longer.It is time-consuming to carry out the life test under normal conditions,and the cost is very expensive.Therefore,the researchers introduced the censoring test.Wu and Kus proposed progressive first failure censoring which is a new type and not only satisfied the need of saving the time for large sample of progressive censoring but also satisfied the need of studying both the failed product and the non-failed product of first failure censoring.The generalized inverse exponential distribution(GIED)was proposed by Abouammoh and Alshingiti in 2009.As the name implies,this is a mixed distribution of generalized exponential distribution and generalized inverse distribution.The researchers studied the generalized inverse exponential distribution based on various life tests.The object of this paper is the generalized inverse exponential distribution based on the progressive first failure censoring samples.According to the framework of this paper,firstly we give the basic conceptions of progressive first failure censoring,generalized inverse exponential distribution,stress intensity model,generalized inference and the likelihood ratio test.Then we study the statistical inference of the generalized inverse exponential distribution of the first-failure successive censored samples,including point estimation and interval estimation.Among them,the point estimates are maximum likelihood estimation and inverse estimation,and Monte Carlo simulation shows that inverse estimation is superior to maximum likelihood estimation.The interval estimation is the exact interval estimation of scale parameters and the generalized confidence interval estimation of shape parameters and other important quantities.The simulated coverage of the proposed confidence interval is basically consistent with the nominal coverage under 90%and 95%quantile simulation.Finally,the statistical inference of the stress-strength model is given,including point estimation,interval estimation and parameter test.It is divided into the case where the scale parameters are equal and uneq,ual,and an example is given to illustrate the superiority of generalized confidence interval estimation.