MIE360 15 Discrete Input Distn

MIE360 15 Discrete Input Distn - MIE360 Computer Modeling...

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MIE360 Computer Modeling and Simula t io n Lecture Notes Daniel Frances © 2010 1 Overview of Input Distribution Fitting This portion of the course will assume that the data is IID, and it will explain how the specialized distribution fitting software packages work. The following flow chart will help. Discrete Type of random variable Select Next distribution Use Maximum Likelihood Estimation to determine the distribution parameters that best fit the data Perform a Chi-square Goodness of Fit test to determine the Confidence of the test. More Distributions? Is there an acceptable distribution? Produce Graphs and Reports Produce an Empirical Distribution Select Next distribution Use Maximum Likelihood Estimation to determine the distribution parameters that best fit the data Perform a Chi-Square OR Kolmogorov–Smirnov OR Andersen-Darling Goodness of Fit test to determine the Confidence of the test. More Distributions? Is there an acceptable distribution? Produce Graphs and Reports Produce an Empirical Distribution Yes No Continuous Yes No Yes No Yes No
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Lecture Notes Daniel Frances © 2010 2 We will first cover the left side of the flowchart – for discrete data, and then return to deal with continuous distributions Maximum Likelihood Estimation Most standard distributions have 1-3 parameters, so how should we go about designing the distribution? Assume for a moment that we are given a set of data X 1 , X 2 , …., X n from the data it appears that it takes discrete values {0, 1, 2, 3, 4…} we draw a histogram by comparing with the palate it looks like the geometric distribution Pdf(x)= p(1-p) x What value of p should we assign? Suppose we superimpose the histogram with “real” geometric distributions As we change p, some bars come closer, others go further apart. What criterion should we use? o minimize sum of squares of differences between Pdf(x) and (f x /n)? o minimize sum of absolute differences? o maximize likelihood of sample? The first two are easy to understand but hard to compute The last one – maximum likelihood is harder to grasp, but relatively easier to compute! After the winning ticket was revealed, many people wonder what the likelihood is of the winning ticket
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This note was uploaded on 09/20/2011 for the course MIE 360 taught by Professor D.frances during the Fall '10 term at University of Toronto.

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MIE360 15 Discrete Input Distn - MIE360 Computer Modeling...

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