定时截尾样本下三参数Weibull分布修正矩估计的强相合性

Strong Consistency of Modified Moment Estimation for Three Weibull Distributions under Type I Censored Samples

摘要: 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, 得出结论: 若所研究的分布满足条件, 修正矩估计强相合于参数真值. 最后证明了当形状参数, 即失效率增加时, 三参数威布尔分布满足条件, 即MME是强相合的.

Abstract: 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 is given and it is proved that if meets condition , then the MME is strong consistent. Lastly, when , is proved to satisfy the condition . Thus the MME \wh\theta_1,\wh\theta_2,\wh\theta_3 is strong consistent provided that the shape parameter \delta\geq 1.