期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2003
卷号：65
期号：02
出版社：Indian Statistical Institute
摘要：Consider a mixture \(G(\cdot)=\int_SF_\theta(\cdot)\,dH(\theta)\). In this paper we derive some bounds on the uniform (Kolmogorov) distance \(\Delta(F_{\theta_0},G)\equiv\sup_x|F_{\theta_0}(x)-G(x)|\) for some convenient choices of \(\theta_0\). In particular, we identify an optimal \(\theta_0\). We illustrate the results by some examples, and show that these new bounds can often be computed easily, and that they improve some known bounds in many instances. Some applications in reliability theory are also described.
关键词：Hazard rate stochastic order, relative aging stochastic order, TP\(_2\) and RR\(_2\) properties, length-biased distribution
