A Study Of The Parametric Inference For Renewal Geometric Processes And It's Application

In the statistical analysis of a series of events,or in the modeling of the successive operating times for a repairable system,considering that many system can maintain their status over a period of time,Liang Xiaolin put forward renewal-geometric process on the basis of staged degeneration,which is more practical and of higher applicability than renewal process and geometric process.Based on existing theory of renewal-geometric process,this thesis has mainly done the following work:At first,based on the concepts of renewal-geometric process and probability statistics theory,this thesis has put forward two primary theorems,then got the testing method of renewal-geometric process.As for a certain renewal-geometric process,it has also constructed its conditional linear regression model.Secondly,this thesis has made the parametric estimation of conditional linear model by using change points test,and has briefly analyzed the property of some parameters.At the same time,through numerical simulation,it has also testified the validity of testing method of renewal-geometric process and the parametric estimation.Then,considering that Lasso-type method can operate variable selection and parametric estimation at the same time,the original linear model has been converted into Lasso-type problems with appropriate auxiliary variables.It has also combined the two-step parametric estimation into one.By contrasting the numerical simulation results of Lasso-type and Adaptive Lasso methods,this thesis has found that these two methods can be applied to the parametric estimation of renewal-geometric process,but Adaptive Lasso is more effective.At last,this thesis has analyzed actual data by using the two methods,and contrasting the fitting results of renewal-geometric process,geometric process and renewal process.It turns out that the renewal-geometric process based on change points test has better fitting results than other models.