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. |
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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(Xn≤dYnY≤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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