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)

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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

Tags

DTIC Thesaurus Topics

  • Air Force
  • Classification
  • Convolution
  • Distribution Functions
  • Inequalities
  • Integrals
  • Intervals
  • Military Research
  • New York
  • Probability
  • Random Variables
  • Reliability
  • Scientific Research
  • Security
  • Stochastic Processes
  • Survival
  • Universities

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Materials Science and Engineering.
  • Wave Propagation and Nonlinear Chaotic Dynamics.