IEOR 165 Lecture 12 June 18 2009

IEOR 165 Lecture 12 June 18 2009 - Normal Dist ribution...

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Normal Distribution = - - fDx 12πσe x μ22σ2 , estimate μ σ ; , = = - - = - == - fx1 xn μ σ2 i 1n12πσe x μ22σ2 12πσ2n2e i 1nx μ22σ2 ; , =- - - = - ; , = * = - lnfx1 xn μ σ2 n2ln2π n2lnσ2 i 1nx μ22σ2ddulnfx1 xn μ σ2 1σ2 i 1nx = → = = μ 0 μMLE 1ni 1nxi ; , =- * + = - = → = = - ddσlnfx1 xn μ σ2 n 1σ 1σ3i 1nx μ2 0 σMLE2 1ni 1nx μMLE2 Then use these parameters and calculate the pi - , = - yi 1 yi pi yi 1yifDydy = < - < - PD yi PD yi 1 = - ( - ) Fyi F yi 1 Excel: Use NORMDIST ( , , , ) yi μMLE σMLE TRUE . This will give us the probabilities for each block. This assumes for –infinity and on. So F(y1) = 0!!! Because we want to start from 0 Weibull Distribution = - - - - , ≥ ; , > fx γαx μαγ 1e x μαγ x μ γ α 0 = assume μ 0 = * - - - = - - = - - = fx cα xc 1αc 1e xcαc cxc 1αce xcαc cθxc 1e xcθ where θi αc ; , = * = - * - = fx1 xn θ c cθn i 1nxic 1 e i 1nxicθ ; , = - + - = - = lnfx1 xn θ c nlnc nlnθ c 1i 1nlnxi 1θi 1nxic ; , =-
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IEOR 165 Lecture 12 June 18 2009 - Normal Dist ribution...

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