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Lecture E2 (2022-09-27): Random-Variate Generation
IEE 475: Simulating Stochastic Systems
English - September 28, 2022 04:46Courses Education simulation stochastic des dess discrete event system industrial engineering modeling Homepage Download Apple Podcasts Google Podcasts Overcast Castro Pocket Casts RSS feed
In this lecture, we review pseudo-random number generation and then introduce random-variate generation by way of inverse-transform sampling. In particular, we start with a review of the two most important properties of a pseudo-random number generator (PRNG), uniformity and independence, and discuss statistically rigorous methods for testing for these two properties. For uniformity, we focus on a Chi-square/Chi-squared test for larger numbers of samples and a Kolmogorov–Smirnov (KS) test for smaller numbers of samples. For independence, we discuss autocorrelation tests and runs test, and then we demonstrate a runs above-and-below-the-mean test. We then shift to discussing inverse-transform sampling for continuous random variates and discrete random variates and how the resulting random-variate generators might be implemented in a tool like Rockwell Automation's Arena.