In most probability texts, it is explained how to find the PDF for the 
th order statistic, assuming the random variables are iid, and you could use this PDF to find the CDF.
But what happens if the random variables are independent but not identically distributed? A bit of searching gave me the Bapat–Beg theorem, proved in 1994.
Fascinating. :) There's also a formula derived for the CDF of an iid set of random variables.
But what happens if the random variables are independent but not identically distributed? A bit of searching gave me the Bapat–Beg theorem, proved in 1994.
Fascinating. :) There's also a formula derived for the CDF of an iid set of random variables.
The kth Order Statistic: Independent but NOT Identically Distributed
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