二元相依Weibu11分布的参数估计

Estimation of Parameters For A Dependent Bivariate Weibull Distribution

摘要: 考虑生存函数为\barF\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\,x_i>0,θ_i>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 \barF\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 x_iθ_i＞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.