Let Y 1 < Y 2 < < Y n be the order statistics
Question:
Let Y1 < Y2 < · · · < Yn be the order statistics of a random sample from a uniform distribution on (0, θ), where θ > 0.
(a) Show that Λ for testing H0 : θ = θ0 against H1 : θ ≠ θ0 is Λ = (Yn/θ0)n, Yn ≤ θ0, and Λ =0 if Yn > θ0.
(b) When H0 is true, show that −2 logΛ has an exact χ2(2) distribution, not χ2(1).
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a Since Y1 Y2 Yn has an exact 2 distribution with n 1 degrees of freedom b lnY10 Y20 ...View the full answer
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Related Book For 
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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