Transcription of Chapter 2. Order Statistics
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Chapter 2. Order Statistics
1 Chapter 2. Order Statistics1 The Order StatisticsFor a sample of independent observationsX1, X2, .. , Xnon a distributionF, the orderedsample valuesX(1) X(2) X(n),or, in more explicit notation,X(1:n) X(2:n) X(n:n),are called the Order Statistics . IfFis continuous, then with probability 1 the Order statisticsof the sample take distinct values (and conversely).There is an alternative way to visualize Order Statistics that, although it does notnecessarily yield simple expressions for the joint density, does allow simple derivation of manyimportant properties of Order Statistics .
Chapter 2. Order Statistics 1 The Order Statistics For a sample of independent observations X 1,X 2,...,X n on a distribution F, the ordered sample values X (1) ≤ X ... for many useful statistics, the most natural and efficient representations are in terms of order statistics. Examples are the extreme values X 1:n and X n:n and the sample range X
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