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Order Statistics PDF

  1. Oct 3, 2009 #1

    Suppose that we have the following set of independent and identically distributed RVs: [tex]\gamma_1,\,\gamma_2,\,\ldots,\,\gamma_M[/tex]. Arranging them in descending order as: [tex]\gamma_{1:M}\ge\gamma_{2:M}\ge\cdots\ge\gamma_{M:M}[/tex]. Now suppose we select the largest [tex]m\leq M[/tex] order statistics. What is the PDF of the selected set? Mathematically:


    Thanks in advance
  2. jcsd
  3. Oct 4, 2009 #2


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    What would f be for m = 1? How do you get there?
  4. Oct 4, 2009 #3

    where [tex]F_{\gamma}(\gamma)[/tex] is the CDF of the original set of RVs.

    But when we pick a subset of the [tex]m^{\text{th}}[/tex] largest order statistics, how can we treat the statistics? I mean I have the final answer from books and papers, but I didn't understand how they derive it.
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