[問題] most powerful test
Wackerly 習題求解
Let Y_1 ... Y_n denote a random sample from a uniform distribution over the
interval (0, θ)
Find the most powerful α-level test for testing H_0 : θ = θ_0
against θ = θ_a, where θ_a < θ_0
嘗試做到
L(θ_0 ) / L(θ_a) = (θ_a / θ_0 ) ^ n *
I_[y_(1), θ_0] ( y(n) ) / I_[y_(1), θ_a] ( y(n) )
= (θ_a / θ_0 ) ^ n if y_(n) < θ_a
< k*
undefined if y_(n) > θ_a
然後不知道該怎麼做下去...
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