The joint pdf of three or more order statistics is given by $f_{x_{(1)},x_{(2)},...x_{(n)}}(x_1,x_2,..x_n)=n! f(x_1)f(x_2)..f(x_n) $

probability statistics probability-distributions order-statistics

The joint pdf of three or more order statistics is given by $f_{x_{(1)},x_{(2)},...x_{(n)}}(x_1,x_2,..x_n)=n! f(x_1)f(x_2)..f(x_n) , \ -\infty<x_1<x_2<...<x_n<\infty $ How can I derive this? I have derived for the bivariate case. Help!


This is a standard result available in textbooks covering order statistics.

Here is a proof from Introduction to the Theory of Statistics (3rd edition) by Mood-Graybill-Boes:

(Check the second page)

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