[問題] 請問一題最強力檢定
Let X_1, ... X_n be random samples from Gamma distribution with density
function f(x) = Γ(ν)^(-1) β^(-ν) x^(ν-1) exp{-x/β} I_(0,∞)(x).
ν is known, β unknown.
Construct a uniformly most powerful test, with significance level α, for
testing the hypothesis
H0: β 屬於 {0.5, 1, 1.6, 1.7, 2}
H1: β 屬於 {2.5, 3, 6, 8, 10}
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我的想法是導一個H0: β≦2 和 β>2 的UMPT
但是拒絕域決定後(應該是長成ΣX_i > C 的形式)
我應該用H0中那個數字當做虛無假設來決定C的值呢?
是2嗎? 感謝解答<(_ _)>
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