摘要:
考虑生存函数为$\bar{F}\left(x_1, x_2\right)=\exp \left\{-\left[\left(x_1^{1 / \alpha} / \theta_1\right)^{1 / \delta}+\left(x_2^{1 / \alpha} / \theta_2\right)^{1 / \delta}\right]^\delta\right\}$,xi>0,θi>0,i=1,2,α>0,0<δ≤1的二无相依Weibull分布。基于在Ⅰ型截尾情形下两个元件与串联系统的寿命试验数据,本文给出了未知参数θ1,θ2,α和 δ 的估计,并讨论了这些估计的渐近性质。本文还给出了随机模拟的结果。
Abstract:
Consider a dependent bivariate Weibull model whose survival function is $\bar{F}\left(x_1, x_2\right)=\exp \left\{-\left[\left(x_1^{1 / \alpha} / \theta_1\right)^{1 / \delta}+\left(x_2^{1 / \alpha} / \theta_2\right)^{1 / \delta}\right]^\delta\right\}$,with xiθi＞0,（i=1,2） α＞0 and 0＜δ＜1 Based on the data of both components and series systems experiments under type I censoring, estimators of the unknown parameters θ1,θ2,αand δ are given, their asymptotic properties are discussed also. A simulation result is given, too.
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