摘要
设｛Ｘｎ，ｎ≥１｝为同分布负相协（Ｎｅｇａｔｉｖｅｌｙ Ａｓｓｏｃｉａｔｅｄ简记为 ＮＡ）随机变量序 列，ｆ（ｘ）为Ｘ１的概率密度函数．基于样本Ｘ１，Ｘ２，…，Ｘｎ，本文构造了密度函数ｆ（ｘ）的 核估计，并在适当条件下证明了其ｒ阶平均相合、逐点强相合和一致强相合特性．作为在 可靠性问题中的应用，本文末利用ＮＡ样本构造了生存函数和失效率的自然估计，并讨论了其相应的相合性．
Let be a sequence of identically distributed and negatively associated (NA) variables with probability density function f(x). Based on NA samples, the kernel estimator for f(x) is constructed, and the consistency in r-order mean, the pointwise strong consistency and strong uniform consistency are shown under suitable conditions. Finally) as the application in reliability problems, the empirical survival function and the kernel-type failure rate estimator are proposed, and the relative consistencies are disscussed.
出处
《系统科学与数学》
CSCD
北大核心
2001年第1期79-87,共9页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金!(19671078
19971085)
中国科学院特别支持费资助
