考虑生存函数为$\overline{F}(x_1,x_2)=\exp \{-[(\frac{x_1^{\frac{1}{\alpha }}}{{\theta }_1}{)}^{\frac{1}{\delta }}+(\frac{x_2^{\frac{1}{\alpha }}}{{\theta }_2}{)}^{\frac{1}{\delta }}{]}^{\delta }\}$, $x_i>0$, $\alpha >0$, $1\ge \delta >0$, ${\theta }_i>0(i=1,2)$的 二元威布尔分布,提出${\theta }_1,{\theta }_2,\alpha ,\delta$的估计并讨论了它们 的渐近性,最后作模拟计算,得出了参数估计的渐近效.

Consider the bivariate dependent Weibull distribution with reliability function $\overline{F}(x_1,x_2)=\exp \{-[(\frac{x_1^{\frac{1}{\alpha }}}{{\theta }_1}{)}^{\frac{1}{\delta }}+(\frac{x_2^{\frac{1}{\alpha }}}{{\theta }_2}{)}^{\frac{1}{\delta }}{]}^{\delta }\}$, $x_i>0$, $\alpha >0$, $1\ge \delta >0$, ${\theta }_i>0(i=1,2)$ This article proposes moment-type estimates $\widehat{{\theta }_1},\widehat{{\theta }_2},\hat{\alpha },\hat{\delta }$ for ${\theta }_1,{\theta }_2,\alpha ,\delta$ and discusses their asymptotic properties. Numerical simulation results are given to demonstrate the asymptotic efficiency of the estimates.