应用概率统计
應用概率統計
응용개솔통계
CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS
2013年
1期
31-41
,共11页
三参数威布尔分布%定时截尾样本%修正矩估计%强相合
三參數威佈爾分佈%定時截尾樣本%脩正矩估計%彊相閤
삼삼수위포이분포%정시절미양본%수정구고계%강상합
Three-parameter Weibull distribution%type I censored samples%the modified moment estimators%strong consistent
本文讨论了定时截尾样本下三参数Weibull分布修正矩估计(MME)的强相合性.首先证明了修正样本矩的强相合性.然后给出了条件(L),得出结论:若所研究的分布F(x;θ1,θ2,θ3)满足条件(L),修正矩估计θ1,θ2,θ3强相合于参数真值.最后证明了当形状参数δ≥1,即失效率增加时,三参数威布尔分布Wei(x;β,δ,γ)满足条件(L),即MME是强相合的.
本文討論瞭定時截尾樣本下三參數Weibull分佈脩正矩估計(MME)的彊相閤性.首先證明瞭脩正樣本矩的彊相閤性.然後給齣瞭條件(L),得齣結論:若所研究的分佈F(x;θ1,θ2,θ3)滿足條件(L),脩正矩估計θ1,θ2,θ3彊相閤于參數真值.最後證明瞭噹形狀參數δ≥1,即失效率增加時,三參數威佈爾分佈Wei(x;β,δ,γ)滿足條件(L),即MME是彊相閤的.
본문토론료정시절미양본하삼삼수Weibull분포수정구고계(MME)적강상합성.수선증명료수정양본구적강상합성.연후급출료조건(L),득출결론:약소연구적분포F(x;θ1,θ2,θ3)만족조건(L),수정구고계θ1,θ2,θ3강상합우삼수진치.최후증명료당형상삼수δ≥1,즉실효솔증가시,삼삼수위포이분포Wei(x;β,δ,γ)만족조건(L),즉MME시강상합적.
This paper discussed the strong consistency of the modified moment estimation (MME) of the parameters in the three-parameter Weibull distribution under type I censored samples. Firstly, the strong consistency of the modified sample moments are proved. Then a condition (L) is given and it is proved that if F(x;θ1,θ2,θ3) meets condition (L), then the MME is strong consistent. Lastly, when δ ≥ 1, Wei(x;β,δ,γ) is proved to satisfy the condition (L). Thus the MMEθ1,θ2,θ3 is strong consistent provided that the shape parameterδ≥1.
