Student's t Distribution

Discussion in 'Scientific Statistics Math' started by Maury Barbato, Dec 23, 2010.

  1. Hello,
    let T_n be a random variable with a Student's t
    distribution with n degrees of freedom.
    For a fixed a > 0, set

    c_n = P(T_n >= a).

    Almost all the tables seem to suggest that {c_n} is a
    decreasing sequence, but I couldn't give a proof of this
    fact. Do you know a proof?

    Thank you very much fro your help.
    My Best Regards,
    Maurizio Barbato

    PS Remember that T_n converges in distribution to the
    standard normal, so that {c_n} converges to phi(-a),
    where phi is the cumulative distribution of the standard
    normal.
     
    Maury Barbato, Dec 23, 2010
    #1
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  2. Maury Barbato

    C Hanck Guest

    No, but I would try to show that the derivative of the cdf wrt the
    degrees of freedom is positive for all a>0, although I do not know if
    that is analytically feasible, in view of the characterization with
    the hypergeometric function etc.

    Christoph
     
    C Hanck, Dec 24, 2010
    #2
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  3. Maury Barbato

    C Hanck Guest

    I just tried it in MAPLE, looks feasible.

    Christoph
     
    C Hanck, Dec 24, 2010
    #3
  4.  
    Maury Barbato, Dec 24, 2010
    #4
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