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.