1. On the skewness of order statistics in multiple-outlier models
- Author
-
Subhash C. Kochar and Maochao Xu
- Subjects
Independent and identically distributed random variables ,Statistics and Probability ,proportional hazard rate ,62G30 ,Exponential distribution ,decreasing failure rate ,Open problem ,General Mathematics ,skewness ,k-out-of-n system ,star order ,01 natural sciences ,010104 statistics & probability ,62N05 ,Probability theory ,Statistics ,Applied mathematics ,exponential distribution ,62D05 ,0101 mathematics ,Mathematics ,right spread order ,Order statistic ,010102 general mathematics ,Exponential function ,Skewness ,Outlier ,Dispersive order ,Statistics, Probability and Uncertainty ,60E15 - Abstract
Kochar and Xu (2009) proved that a parallel system with heterogeneous exponential component lifetimes is more skewed (according to the convex transform order) than the system with independent and identically distributed exponential components. In this paper we extend this study to the general k-out-of-n systems for the case when there are only two types of component in the system. An open problem proposed in Pǎltǎnea (2008) is partially solved.
- Published
- 2011