10SimHw12Solution

# 10SimHw12Solution - IEOR E4404.001 SIMULATION Prof. Mariana...

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IEOR E4404.001 SIMULATION Prof. Mariana Olvera-Cravioto Assignment #12 Solutions 1. We run the K-S test on several distributions: Gamma: a = 3 . 26, b = 0 . 40, p = 0 . 73. There is not enough evidence to reject the null hypothesis. Lognormal: μ = 0 . 11, σ = 0 . 61, p = 0 . 16. We reject the null hypothesis when α = 5%. Weibull: a = 1 . 49, b = 2 . 00, p = 0 . 97. There is not enough evidence to reject the null hypothesis. Out of the ones we tried, the Weibull distribution provides the best ﬁt. 2. We perform the Chi-Square test with a binomial B (4 , 0 . 37) and with a poisson P (1 . 492). In the case of the binomial distribution, we do not reject the null hypothesis. 3. (a) We have L ( a ) = { 0 if a < max( { X i } ) 1 a n otherwise . Since 1 a n is always greater than 0, we want to maximize L ( a ) subject to a max( { X i } ). Thus, the MLE is a = max( { X i } ) (b) L ( a ) = 0 if b - a max( { X i } ) - min( { X i } ) 0 if a min( { X i } ) 1 ( b - a ) n otherwise

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## This note was uploaded on 11/17/2010 for the course IEOR IEOR 4404 taught by Professor C during the Spring '10 term at Columbia.

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10SimHw12Solution - IEOR E4404.001 SIMULATION Prof. Mariana...

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