作者austinyung (ATN)
看板Statistics
標題Re: [問題] Inverse Probability Integral Transfo …
時間Wed Sep 23 23:12:51 2009
※ 引述《lookinforyou (Loving Kitty =))》之銘言：
: 1. Show that the inverse probability integral transformation for the
: exponential(theda) distribution is y = -(theda)ln(1-u)
: <f(y) = exp[-y/theda] / theda>
: 2. (continuation) If u is uniform(0, 1), deduce that -ln u is exponential(1)
: or gamma(1); and that -2ln u is chi square(2)
: 第一題我有導出來了 不過第二題一直想不出來...
: 麻煩各位高手了...謝謝
u-->uniform(0, 1)
let -ln u = t
u=e^(-t) du/dt=-e^(-t)
h(t)=f(u)|-e^(-t)|=e^(-t) ------>Exp(1)
--
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◆ From: 59.104.229.47
1F：→ west1996:最後一行等號右邊應該是f(u)？ 09/23 23:15
※ 編輯: austinyung 來自: 59.104.229.47 (09/23 23:25)
2F：→ austinyung:恩..已改正 09/23 23:26
3F：推 ksherry:第二題一樣算法 算出來是gamma (1,2) = 卡方2 09/23 23:26
4F：→ lookinforyou:THANK YOU!!! 09/26 02:26