逐次定数截尾数据下ZZ分布的参数估计

Parameter Estimation of ZZ Distribution under Progressive Type-II Censored Data

对于设计寿命之前很少失效,设计寿命之后失效比例大幅增加的一类存储产品,其寿命变量用ZZ分布来描述较为合适。基于逐次定数截尾样本,首先利用泰勒展式将似然函数中的非线性部分转化为线性表达,使似然方程可解,进而得到参数的近似极大似然估计。其次,运用最佳线性无偏估计法,给出了参数无偏估计的一般解析表达式,同时针对两种特殊逐次定数截尾样本,进一步化简了估计的表达形式,且为便于使用,给出了计算所需数表的构造公式。最后对两种估计做了数值模拟比较,结果表明ZZ分布的最佳线性无偏估计优于近似极大似然估计。

ZZ distribution is suitable to describe the life variable of a type of storage products that rarely fail before a given design life,and the proportion of failures has increased significantly after the design life.Based on a progressive type-II censored sample,firstly using Taylor′s formula to transform the the nonlinear part of the likelihood function into a linear expression,the likelihood equation is solvable,and the approximate maximum likelihood estimation(AMLE)of the parameter is given.Secondly,using the best linear unbiased estimation(BLUE)method,a general analytical expression of the parameter is given.At the same time,the expression form of the estimation is further simplified for two kinds of special progressive type-II censored sample and the required number table is constructed for the convenience of use.Finally,a numerical comparison of the two methods is performed,and the results show that the best linear unbiased estimation of ZZ distribution is better than the approximate maximum likelihood estimation.