一类非正态总体未知参数的Bayes假设检验

The Bayesian Hypothesis Testing of a few Non-normal Parameters

利用贝叶斯统计思想总结了两种常见的假设检验方法,在此基础上针对H0∶θ=0θ,θ≠θ0这样的假设检验问题,提出了构造参数θ的否定域,即求出参数θ的置信概率为1-α的最大后验区间,区域Θ-D为参数θ的否定域,检验θ是否在否定域内,若在就否定H0,运用这样的思想对其进行检验.并且讨论了γ-分布与β-分布,β-分布与F-分布,γ-分布与χ2-分布之间的相互关系,借助以上的性质,研究三类非正态总体指数分布、二项分布和泊松分布的未知参数的贝叶斯假设检验,给出了相应的否定域.

In this paper, the thought of Bayesian statistics is employed to sum up two kinds of common hypothesis testing, on this basis, lighting on the hypothesis testing H0： θ = θ0 ,H1 ≠θ0, the construction of parameter θ of the rejection region is put forward, that is to obtain the largest posterior interval of fiducial probability 1 - α of parameters θ, and the rejection region of parameter θ in region ⊙ - D. Then test if is in the rejection region. If it is, deny H0. The connection of γ - distribution and β - distribution ,β - distribution and F - distribution ,γ- distribution and χ^2 - distribution are also discussed. With the above result, the Bayesian hypothesis testing of three kinds of Nonnormal Parameters, such as Exp（λ） ,b（n,p） and P（λ） are studied and their rejection regions are obtained.