论文标题
在$ pr（x <y <z）$及其概括的UMVUE和封闭式贝叶斯估算器上
On the UMVUE and Closed-Form Bayes Estimator for $Pr(X<Y<Z)$ and its Generalizations
论文作者
论文摘要
本文考虑了$ pr（x <y <z）$的参数估计及其基于几个著名的单参数和两参数连续分布的概括。 It is shown that for some one-parameter distributions and when there is a common known parameter in some two-parameter distributions, the uniformly minimum variance unbiased estimator can be expressed as a linear combination of the Appell hypergeometric function of the first type, $F_{1}$ and the hypergeometric functions $_{2}F_{1}$ and $ _ {3} f_ {2}。$基于共轭伽玛先验和Jefferys在平方错误损耗函数下的非信息性先验的贝叶斯估计器也作为线性组合给出，$ _ {2} f _ {2} f _ {1} $ {1} $和$ f_ {1}。 $ f_ {1} $函数也提出了。在模型的概括和扩展中，进一步表明，UMVUE可以表示为lauricella系列的线性组合，$ f_ {d}^{（n）}，$和概括的高几点功能，$ _ {p} f_ {q} f_ {q}，$ sy $ f _ $ f _ $ f_ {1} $} $ {1} $ {1} $ {2一般的封闭形式贝叶斯估计量也作为收敛的无限系列，涉及$ f_ {d}^{（n）}。$，以衡量UMVUE的性能和$ P $的封闭式贝叶斯估计器对其他知名估计器，对其他知名估计器，最大的可能性估计，最大的可能性估计值，Lindley近似估计值估计和Markov Chablo Marte Monte Monte Cared $ P $ $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P $ P》中供$ py估计，供$ py估计。另外，还构建了渐近置信区间和贝叶斯最高概率密度可靠间隔。
This article considers the parametric estimation of $Pr(X<Y<Z)$ and its generalizations based on several well-known one-parameter and two-parameter continuous distributions. It is shown that for some one-parameter distributions and when there is a common known parameter in some two-parameter distributions, the uniformly minimum variance unbiased estimator can be expressed as a linear combination of the Appell hypergeometric function of the first type, $F_{1}$ and the hypergeometric functions $_{2}F_{1}$ and $_{3}F_{2}.$ The Bayes estimator based on conjugate gamma priors and Jefferys' non-informative priors under the squared error loss function is also given as a linear combination of $_{2}F_{1}$ and $F_{1}.$ Alternatively, a convergent infinite series form of the Bayes estimator involving the $F_{1}$ function is also proposed. In model generalizations and extensions, it is further shown that the UMVUE can be expressed as a linear combination of a Lauricella series, $F_{D}^{(n)},$ and the generalized hypergeometric function, $_{p}F_{q},$ which are generalizations of $F_{1}$ and $_{2}F_{1}$ respectively. The generalized closed-form Bayes estimator is also given as a convergent infinite series involving $F_{D}^{(n)}.$ To gauge the performances of the UMVUE and the closed-form Bayes estimator for $P$ against other well-known estimators, maximum likelihood estimates, Lindley approximation estimates and Markov Chain Monte Carlo estimates for $P$ are also computed. Additionally, asymptotic confidence intervals and Bayesian highest probability density credible intervals are also constructed.
