Re: [問題] 關於mle的問題
※ 引述《fifs (^^)》之銘言:
: let X1,X2,...,Xn be a random sample from the uniformly distrubution.
: f(x)=1/θ θ<x<2θ , θ>0.
: Show that (1/2)Y1+(1/4)Yn is one mle of θ , where Y1,Y2,...Yn
: represent the order statistics of the random sample.
: 這是我們的做法
: 1
: likelihood function is L(θ)=-----I[(1/2)Yn,Y1](θ) where I is indictor
: θ^n function.
: 明顯的 L(θ)為一個θ遞減函數 ,for all θ>0.
: 所以θ的mle為Yn
θ的mle為Yn與Y1
_ _
而常態分配的mle 為 (X , S^2) or (ΣXi ,Σ(Xi-X)^2 )
: 難以想像 為何(1/2)Y1+(1/4)Yn is one mle of θ ??
所以 (1/2)Y1+(1/4)Yn is one mle of θ.
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