Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Note on Stochastic Inequalities

  • Published : 1980.12.01
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Abstract

In this note, we establish a result which characterizes a partial ordering of probability distributions on a partially ordered space by that of conditional distributions. This result is then reduced to prove the conjecture made by Nevius, Proschan and Sethuraman (1977).

Keywords

References

  1. Statistical Theory of Reliability and Life Testing: Probability Models Barlow,R.E.;Proschan,F.
  2. Inequalities Hardy,G.H.;Littlewood,J.E.;Polya,G.
  3. Ann. Statist. v.5 Schur functions in statistics. II. Stochastic majorization Nevius,S.E.;Proschan,F.;Sethuraman,J.
  4. Ann. Probability v.5 Stochastic inequalities on partially ordered space Kamae,T.;Krengel,U.;O'Brien,G.L.
  5. Ann. Math. Statist. v.36 The existence of probability measures with given marginals Strassen,V.