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# hw11 - IEOR 4404 Simulation Prof Mariana Olvera-Cravioto...

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IEOR 4404 Assignment #11 Simulation December 7, 2006 Prof. Mariana Olvera-Cravioto Page 1 of 2 Assignment #11 – due December 11th, 2006 1. The p -value of the Kolmogorov-Smirnov test is defined as p -value = P ˆ F ( D n > d ) where ˆ F is the hypothesized distribution for the iid observations X 1 , X 2 , . . . , X n and D n = sup x {| F n ( x ) - ˆ F ( x ) |} . The p -value measures the probability that we are correct in accepting the hypothesis that the X i ’s have distribution ˆ F based on a result D n = d . It can be shown that P ˆ F ( D n > d ) = P max 0 y 1 # i : U i y n - y d for all continuous distributions ˆ F , where the U i ’s are iid Uniform(0,1) random variables. Generate the values of 10 independent exponential random variables each having mean 2 and compute their Kolmogorov-Smirnov statistic, D n . Use simulation to approximate the p -value of the test, that is, if the value of the statistic is D n = d , approximate the quantity P max 0 y 1 # i : U i y n - y d via simulation.

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hw11 - IEOR 4404 Simulation Prof Mariana Olvera-Cravioto...

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