On Mixtures of Pdlya-Laguerre Frequency Functions of Finite Class & Its Application to System Reliability
In this paper a convex family of distribution functions, naturally arising in time homogeneous Markov processes is discussed, hi section 1, the extreme points of this family are identified and shown how these span the whole of the family. This family contains the family of all finite mixtures of exponential distributions and is contained in the family of all distribution functions which are finite linear combinations of exponential distributions. In section 2 these three families are compared. In section 3 three methods of establishing membership in the family are presented and some closure properties of the family also demonstrated. In section 4 the family is characterised as the lifetime distributions of time homogenous Markov processes on partial orderings with terminal points. In section 5 the Cartesian products of Markov processes on partial orderings have been defined and briefly investigated. In section 6 the study has been restricted to Markov processes on Boolean lattices, the interesting connection of these with reliability of coherent systems presented. Finally this connection is used to give a new proof of a combinatorial lemma due to Sperner.
Pdlya-Laguerre Frequency Functions Markov Processes Convex Sets and their Extreme Points Newtons Interpolation Partial Ordering Boolean lattices Systems Reliability
ASSAD JALALI
Statistics Research Group, School of Business and Economics, Swansea University, Swansea, SA2 8PP, UK.
国际会议
北京
英文
760-767
2011-06-20（万方平台首次上网日期，不代表论文的发表时间）