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Math Help - Stochastic Orders

  1. #1
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    Stochastic Orders

    I am really desperate for this simple question:

    Assume X and Y are random variables, such that:
    X is "stochastically greater" than Y

    Then by definition:
    E[f(x)] >= E[f(y)] if f(.) is INCREASING

    My question is:

    What is f(.) is decreasing? Does the operator above change, or what?
    Last edited by mr fantastic; November 29th 2009 at 05:13 PM. Reason: Changed post title
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  2. #2
    MHF Contributor

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    Paris, France
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    Quote Originally Posted by aelwany View Post
    I am really desperate for this simple question:

    Assume X and Y are random variables, such that:
    X is "stochastically greater" than Y

    Then by definition:
    E[f(x)] >= E[f(y)] if f(.) is INCREASING

    My question is:

    What is f(.) is decreasing? Does the operator above change, or what?
    f is decreasing iff -f is increasing. This should answer your question.
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  3. #3
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    Thank you very much Laurent. I appreciate your quick reply.
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