Stochastic comparisons of order statistics from gamma distributions

  • Authors:

  • Sun Lihong;Zhang Xinsheng

  • Affiliations:

  • Department of Statistics, East China Normal University, Shanghai 200062, PR China;Department of Statistics, Fudan University, China

  • Venue:
  • Journal of Multivariate Analysis
  • Year:
  • 2005

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Abstract

Let (X1, X2, ..., Xn) and (Y1, Y2, ..., Yn) be gamma random vectors with common shape parameter α(01,λ2,...,λn), (µ1,µ2,...,µn), respectively. Let X() = (X(1), X(2)..., X(n)), Y() = (Y(1), Y(2),...,Y(n)) be the order statistics of (X1, X2,...,Xn) and (Y1, Y2,...,Yn). Then (λ1, λ2,...,λn) majorizes (µ1, µ2,...,µn) implies that X() is stochastically larger than Y(). However if the common shape parameter α1, we can only compare the the first-and last-order statistics. Some earlier results on stochastically comparing proportional hazard functions are shown to be special cases of our results.