Let Y 1 < Y 2 < < Y n be the order statistics

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Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample of size n from a distribution of the continuous type having distribution function F(x).

(a) What is the distribution of U = 1− F(Yj)?

(b) Determine the distribution of V = F(Yn) − F(Yj) + F(Yi) − F(Y1), where i < j.

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Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

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