A Note on Stochastic Ordering (≤d)
Received:October 26, 1990  
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Fund Project:The Project is supported by the National Natural Science Foundation.
Author NameAffiliation
Hu Nanhua Dept. Math.
Xiamen University 
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Abstract:
      In discussing the convergence in probability (in distribution) of a sequence of random variables, it is often used that if for any n,P{Xn≤Yn ≤Zn} = 1 and (?). It is shown now that the stochastic ordering condition Xn- Y≤dYn- Y≤dXn- Y(XndYnY≤dZn) is a more general dominating condition than P{Xn≤Yn≤Zn}=1 in ensuring the convergence in probability (in distribution) of {Yn}.
Citation:
DOI:10.3770/j.issn:1000-341X.1993.01.012
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