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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.

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

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 $\delta\geq 1$.