Re: [問題] 一題MLE的問題 ~

[janep (XD)]

※ 引述《taldy ()》之銘言：
: A random variable X is said to have a lognormal distribution,if the logarithm
: of X has a normal distribution.Let X1,X2,...,Xn be iid lognormal random
: variables ,thus Yi=lnXi ~N(μ,σ^2).Use invariance principle of maximum
: likelihood estimation to find the MLE of E(Xi) and Var(Xi).
: 有誰知道怎麼解的,回答一下..thx

Y~N(μ,σ^2)

so
           1               1
f(y)= ---------- exp [- -------(y-μy)^2]
      √2πσy          2σy^2


Y=lnX

           1              1                 1
f(x)= ---------- exp [- ------(lnx-μy)^2] ---
       √2πσy         2σy^2              x


let μy=lnx0   σy=ω

           1               1       x
f(x)= ---------- exp {- ------[ln(---)]^2}
      √2πω x          2ω^2     x0

應該可以從這方面去推出來吧..

因為我也是最近才看到這個..所以不太懂..希望對你有幫助..XD

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推 mangogogo:invariance principle of MLE 這才是重點