TP2 Orderings.
Abstract
Uniform stochastic orderings of random variables are expressed as total positivity of density, survival and distribution functions. The orderings are called uniform because each is a stochastic order that persists under conditioning to a family of intervals-for example, the family consisting of all intervals of the form (- infinity,x). This paper is concerned with the preservation of uniform stochastic ordering under convolution, mixing and the formation of coherent systems. A general TP2 result involving preservation of total positivity under integration is presented and applied to convolutions and mixtures, of distribution and survival functions. Logconcavity of distribution, survival and density functions characterizes random variables that preserve the various orderings under addition. Likewise, random variables that preserve orderings under mixing are characterized by TP2 distribution and survival functions. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1984
- Accession Number
- ADA143434
Entities
People
- Frank Proschan
- G. Mimmack
- J. Lynch
Organizations
- Florida State University