November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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4.13 MINIMUM, MAXIMUM, AND ORDER STATISTICS
Consider N random variables 
that are iid with pdf fX(x). The goal in this section is to derive pdfs for the minimum 
(called the first-order statistic), the maximum 
(called the Nth-order statistic), as well as the overall order statistics.
Definition: Order Statistics The order statistics are the random variables 
arranged in increasing order: 
.
There may be some confusion about ordering random variables according to size because they are random and each can assume a range of values. Of course, once we have an actual sample (collection of outcomes) given by 
, they can be ordered according to size. However, ordered random variables 
can be described in a probabilistic sense, as we show now using the cdf transformation method.
Theorem 4.4(Order statistics). ...
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