摘要
本文证明了对于Weibull分布来讲,基于随机截尾数据得到的参数的最大似然估计具有强相合性。
Let (x, i≥1) be i.i.d.r.v'.s with P(x_1≤x)=F(x, α, λ), where α>0, λ>0, F(x, α, λ)=1-e^(-λx^α)(x>0), F(x, α, λ)=0 (x≤0) in which both of α and λ are unknown. Let (y_1, i≥1) be a sequence of independent random variables with P(y_i≤x)=G_i(x), G_i(0)=0(i≥1). Suppose that the two sequences are independent of each other. Set t_i=min(x_i, y_i), δ_i=I(x_i≤y_i) (i≥2), I(A) being the indicator function of A. As well-known, maximum likelihood estimators ■_n and ■_n of α, λ based on data (t_1, δ_1), …, (t_n, s_n) are the solution of the following equations: In the present paper, we have proved the following theorem: ① If there exists x>0 such that ■ 1/n sum 1 to n G_i(x)<1, then ■_n and ■_n are consistent estimators of α and λ respetively. ② If there exists x>0 such that ■ 1/n sum 1 to n G_i(x)<1 and there exist limits ■ 1/n sum 1 to n · G_i(y) for almost all y w.r.t. Lebesgue measure, then both ■_n and ■_n are strongly consistent.
出处
《应用概率统计》
CSCD
北大核心
1989年第3期226-233,共8页
Chinese Journal of Applied Probability and Statistics
