Students of statistics, operations research, and engineering will be informed of simulation methodology for problems in both mathematical statistics and systems simulation. This discussion presents many of the necessary statistical and graphical techniques.A discussion of statistical methods based on graphical techniques and exploratory data is among the highlights of Simulation Methodology for Statisticians, Operations Analysts, and Engineers.For students who only have a minimal background in statistics and probability theory, the first five chapters provide an introduction to simulation.
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 ResourcesAssessing 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