Inference For The Proportional Hazard Model Based On The Generalized Order Statistics

When researching product reliability,people often divide products into repairable and non-repairable products.The so-called repairable product means that when the product loses the specified function,it can be restored by overhauling its function.When the product loses the specified function,it is impossible or uneconomical to repair.If the product is discarded after it fails,the product is said to be unrepairable.If the unrepairable product loses the specified function,the product is said to have failed.Therefore,the study of inference for the proportional hazard model is attracting widespread attention.Kamps(1995)proposed the concept of generalized order statistics(GOS).GOS is a generalization of various commonly used order statistics.Therefore,we can unify the distribution theory of all kinds of order statistics into the distribution theory of GOS.The content discussed in this paper is inference for the proportional hazard model based on the generalized order statistics.This paper first introduces the basic concepts of the proportional hazard model,failure rate,reliability function,Progressively Type-? censored sample,upper record values,generalized order statistics,generalized estimation and replacement methods.Then inference for the proportional hazard model based on the generalized order statistics is studied.Using the probability-integral transformation and the memorylessness of the exponential distribution,the generalized order statistic is transformed into independent and identically distributed random variables,Thereby constructing quasi-samples and pivotal quantity.Then the generalized statistical inference method is used to obtain the generalized pivot quantity of the proportional hazard model parameters,and solve the point estimate of the parameter by inverse estimation method.Then take the Weibull distribution as an example,the corresponding results are obtained.Then derive the generalized confidence interval of the corresponding reliability characteristics of the Weibull distribution.On this basis,we investigate the method of inferring the proportional hazard model based on Progressively Type-? censored sample and upper record values,and take the Weibull distribution as an example to obtain the corresponding specific results.Finally,the inference method based on generalized order statistics for generalized Pareto distribution is studied,and investigate the generalized confidence intervals and point estimates of the parameters of generalized Pareto distribution based on complete samples.Comparison of point estimation with the maximum likelihood estimation and the M estimation method by Monte Carlo simulation method,our point estimation method,that is,the inverse estimation method is good.The simulation coverage of the confidence interval of our method is obtained by 90% and 95% quantile simulation and compared with the boostrap method based on M estimation(Ye's method),it is concluded that our method,whether it is a scale parameter or a shape parameter,compares the coverage of the simulation with the method of Ye,which is closer to the nominal coverage.When the shape parameter ?<0,the length of the interval of our method is closer to the value of the real parameter than the Ye's method.Continue to investigate the point estimation inference method of the generalized Pareto distribution based on upper record values and compare with the maximum likelihood estimation method,and find that our merthod(the inverse estimation method)is better.The simulation coverage of the generalized confidence interval of our method is obtained by 90% and 95% quantile simulation,which is basically consistent with the nominal coverage,indicating that our method is effective.