Chap08Slides - 8-1 CHAPTER 8 Generating Random Variates 8.1

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Unformatted text preview: 8-1 CHAPTER 8 Generating Random Variates 8.1 Introduction................................................................................................2 8.2 General Approaches to Generating Random Variates ....................................3 8.2.1 Inverse Transform...............................................................................................................3 8.2.2 Composition.....................................................................................................................11 8.2.3 Convolution......................................................................................................................16 8.2.4 Acceptance-Rejection.......................................................................................................18 8.2.5 Special Properties.............................................................................................................26 8.3 Generating Continuous Random Variates....................................................27 8.4 Generating Discrete Random Variates.........................................................27 8.4.3 Arbitrary Discrete Distribution...........................................................................................28 8.5 Generating Random Vectors, Correlated Random Variates, and Stochastic Processes ........................................................................................................34 8.5.1 Using Conditional Distributions..........................................................................................35 8.5.2 Multivariate Normal and Multivariate Lognormal................................................................36 8.5.3 Correlated Gamma Random Variates ................................................................................37 8.5.4 Generating from Multivariate Families................................................................................39 8.5.5 Generating Random Vectors with Arbitrarily Specified Marginal Distributions and Correlations...................................................................................................................................................40 8.5.6 Generating Stochastic Processes........................................................................................41 8.6 Generating Arrival Processes .....................................................................42 8.6.1 Poisson Process................................................................................................................42 8.6.2 Nonstationary Poisson Process..........................................................................................43 8.6.3 Batch Arrivals ...................................................................................................................50 8-2 8.1 Introduction Algorithms to produce observations (variates) from some desired input distribution (exponential, gamma, etc.) Formal algorithmdepends on desired distribution...
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Chap08Slides - 8-1 CHAPTER 8 Generating Random Variates 8.1

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