Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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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.)
  • Published : 1996.06.01
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Abstract

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.

Keywords

References

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