Some Positive Dependent Orderings

  • Tae-Sung Kim (Department of Statistics, Won-Kwang University, Iksan City, 570-739, Korea.) ;
  • Song-Ho Kim (Department of Statistics, Anyang University, Anyang City, 430-714, Korea.)
  • 발행 : 1996.06.01

초록

Let X and Y be random vectors in R$^{n}$ . A random vector X is 'more associated' than Y if and only if P(X $\in$ A ∩ B) - P(X $\in$ A)P(X $\in$ B) $\geq$ P(Y $\in$ A ∩ B)-P(Y $\in$ A)P(Y $\in$ B) for all open upper sets A and B. By requiring the above inequality to hold for some open upper sets A and B various notions of positive dependence orderings which are weaker than 'more associated' ordering are obtained. First a general theory is given and then the results are specialized to some concepts of a particular interest. Various properties and interrelationships are derived.

키워드

참고문헌

  1. Statistical Theory of Reliability and Life Testing. To Begin With Barlow, R. E.;Proschan F.
  2. Annal of Statistics v.2 multivariate distributions with exponential minimums Esary, J. D.;Marshall, A. W.
  3. The Annals of Mathematical Statistics v.38 Association of random variables with applications Esary, J. D.;Proschan F.;Wakup, D.W.
  4. Lectures Notes-Monograph Series v.16 Information, censoring, and dependence Topics in Statistical Dependence Institute of Mathematical Statistics Hollander, M.;Proschan, F.;Sconing, J.
  5. The Annals of Mathematical Statistics v.73 Some concepts of dependence Lehmann, E. L.
  6. The Annals Statistics v.15 An ordering for positive dependence Schriever, B. F.
  7. Journal of Multivariate Analysis v.12 A general theory of some positive dependence notions Shaked, M.
  8. The Annals of Institute of Statistical Mathematics v.21 Partial orderings of permutations and monotonicity of a rank correlation statistics Yanagimoto, T.;Okamoto, M.