Objective Bayesian Analysis For The Generalized Logistic Distribution And Doubly Accelerated Degradation Model

Objective Bayesian statistics is an important branch in Bayesian statistics,its theory,method and application have received extensive attention in recent years.This paper mainly studies the statistical inference of the objective Bayesian method in the Logistic distribution as well as in the degradation data analysis.The Logistic distribution is an important distribution in statistics,which has a wide range of applications in geography,hydrology,biology and medicine.To our surprise,there is very little research on the objective Bayesian analysis for the Logisitic distribution in the literature.The propriety problem of posterior distribution of Jeffreys prior and reference prior is systematically studied in this paper,the results of objective Bayesian analysis for the Logistic distribution are developed.Recently,the Wiener process has become an important tool for degradation data analysis.In this paper,a doubly accelerated degradation model based on the Wiener process is proposed,and the objective Bayesian approach is employed to analyze the model.The Jeffreys prior and the reference prior under different orderings are first derived,and the propriety of the posterior distribution under each prior is validated.By simulation study,the proposed Bayesian approach is compared with the Bootstrap method in terms of the mean squared error and the coverage probability.Finally,the approach is applied to analyze a real data example.