SIMULATION METHODOLOGY FOR STATISTICIANS, OPERATIONS ANALYSTS, AND ENGINEERS

Content: MODELING AND CRUDE SIMULATIONDefinition of SimulationGolden Rules and Principles of SimulationModeling: Illustrative Examples and ProblemsThe Modeling Aspect of SimulationSingle-Server, Single-Input, First-In/First-Out (FIFO) QueueMultiple-Server, Single-Input QueueAn Example from Statistics: The Trimmed t StatisticAn Example from Engineering: Reliability of Series SystemsA Military Problem: Proportional NavigationComments on the ExamplesCrude (or Straightforward) Simulation and Monte CarloIntroduction: Pseudo-Random NumbersCrude SimulationDetails of Crude SimulationA Worked Example: Passage of Ships Through a Mined ChannelGeneration of Random PermutationsUniform Pseudo-Random Variable GenerationIntroduction: Properties of Pseudo-Random VariablesHistorical PerspectivesCurrent AlgorithmsRecommendations for GeneratorsComputational ConsiderationsThe Testing of Pseudo-Random Number GeneratorsConclusions on Generating and Testing Pseudo-Random Number GeneratorsSOPHISTICATED SIMULATIONDescriptions and Quantifications of Univariate Samples: Numerical SummariesIntroductionSample MomentsPercentiles, the Empirical Cumulative Distribution Function, and Goodness-of-Fit TestsQuantilesDescriptions and Quantifications of Univariate Samples: Graphical SummariesIntroductionNumerical and Graphical Representations of the Probability Density FunctionAlternative Graphical Methods for Exploring DistributionsComparisons in Multifactor Simulations: Graphical and Formal MethodsIntroductionGraphical and Numerical Representation of Multifactor Simulation ExperimentsSpecific Considerations for Statistical SimulationSummary and Computing Resources Assessing Variability in Univariate Samples: Sectioning, Jackknifing, and BootstrappingIntroductionPreliminariesAssessing Variability of Sample Means and PercentilesSectioning to Assess Variability: Arbitrary Estimates from Non-Normal SamplesBias EliminationVariance Assessment with the Complete JackknifeVariance Assessment with the BootstrapSimulation Studies of Confidence Interval Estimation SchemesBivariate Random Variables: Definitions, Generation, and Graphical AnalysisIntroductionSpecification and Properties of Bivariate Random VariablesNumerical and Graphical Analyses for Bivariate DataThe Bivariate Inverse Probability Integral TransformAd Hoc and Model-Based Methods for Bivariate Random Variable GenerationVariance ReductionIntroductionAntithetic Variates: Induced Negative CorrelationControl VariablesConditional SamplingImportance SamplingStratified Sampling