井冈山大学学报(自然科学版)
井岡山大學學報(自然科學版)
정강산대학학보(자연과학판)
JOURNAL OF JINGGANGSHAN UNIVERSITY(SCIENCE AND TECHNOLOGY)
2015年
4期
7-12
,共6页
刘荣玄%邬四英%张萍
劉榮玄%鄔四英%張萍
류영현%오사영%장평
首失效截尾样本%三参数Pareto分布%UMVUE与PEB估计%样本性质
首失效截尾樣本%三參數Pareto分佈%UMVUE與PEB估計%樣本性質
수실효절미양본%삼삼수Pareto분포%UMVUE여PEB고계%양본성질
first-failure-censoring samples%three-parameter Pareto distribution%UMVUE and PEB estimation%sample properties
在逐步增加首失效截尾样本下,研究三参数Pareto分布族形状参数的一致最小方差无偏估计(UMVUE),在对称平方损失函数下,讨论其 Bayes 估计和参数型经验 Bayes(PEB)估计;按照均方误差(MSE)准则,比较UMVUE与PEB估计的小样本性质;根据形状参数的风险,导出其Bayes估计与PEB估计的大样本性质,并获得它们的收敛速度o (n?1)。
在逐步增加首失效截尾樣本下,研究三參數Pareto分佈族形狀參數的一緻最小方差無偏估計(UMVUE),在對稱平方損失函數下,討論其 Bayes 估計和參數型經驗 Bayes(PEB)估計;按照均方誤差(MSE)準則,比較UMVUE與PEB估計的小樣本性質;根據形狀參數的風險,導齣其Bayes估計與PEB估計的大樣本性質,併穫得它們的收斂速度o (n?1)。
재축보증가수실효절미양본하,연구삼삼수Pareto분포족형상삼수적일치최소방차무편고계(UMVUE),재대칭평방손실함수하,토론기 Bayes 고계화삼수형경험 Bayes(PEB)고계;안조균방오차(MSE)준칙,비교UMVUE여PEB고계적소양본성질;근거형상삼수적풍험,도출기Bayes고계여PEB고계적대양본성질,병획득타문적수렴속도o (n?1)。
We derive the uniformly minimum variance unbiased estimation (UMVUE) of shape parameter of the three-parameter Pareto distribution family based on progressive first-failure-censoring samples. Furthermore, the Bayesian estimation and the parameter-type empirical Bayes (PEB) estimation have been obtained under the symmetric loss function. The small sample properties of UMVUE and the PEB estimation are compared under the mean- square error (MSE) criterion. The large sample properties of the Bayesian estimation and the PEB estimation of the parameters are proved according to the risk of the shape parameter and the convergence rateo(n?1) is obtained. The interval estimations of the parameters in classical statistics and Bayesian statistics are discussed respectively under the same or similar credible level. At last, the precision of the Bayesian interval estimation is better than in classical statistics is illustrated by some numerical simulation results.