作者janep (XD)
看板Statistics
標題Re: [問題] 一題MLE的問題 ~
時間Wed Oct 19 12:24:01 2005
※ 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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1F：推 mangogogo:invariance principle of MLE 這才是重點 10/19 17:02