Simulation Methodology for Statisticians, Operations Analysts, and Engineers, Vol. 1 Book

MODELING AND CRUDE SIMULATION Definition of Simulation Golden Rules and Principles of Simulation Modeling: Illustrative Examples and Problems The Modeling Aspect of Simulation Single-Server, Single-Input, First-In/First-Out (FIFO) Queue Multiple-Server, Single-Input Queue An Example from Statistics: The Trimmed t Statistic An Example from Engineering: Reliability of Series Systems A Military Problem: Proportional Navigation Comments on the Examples Crude (or Straightforward) Simulation and Monte Carlo Introduction: Pseudo-Random Numbers Crude Simulation Details of Crude Simulation A Worked Example: Passage of Ships Through a Mined Channel Generation of Random Permutations Uniform Pseudo-Random Variable Generation Introduction: Properties of Pseudo-Random Variables Historical Perspectives Current Algorithms Recommendations for Generators Computational Considerations The Testing of Pseudo-Random Number Generators Conclusions on Generating and Testing Pseudo-Random Number Generators SOPHISTICATED SIMULATION Descriptions and Quantifications of Univariate Samples: Numerical Summaries Introduction Sample Moments Percentiles, the Empirical Cumulative Distribution Function, and Goodness-of-Fit Tests Quantiles Descriptions and Quantifications of Univariate Samples: Graphical Summaries Introduction Numerical and Graphical Representations of the Probability Density Function Alternative Graphical Methods for Exploring Distributions Comparisons in Multifactor Simulations: Graphical and Formal Methods Introduction Graphical and Numerical Representation of Multifactor Simulation Experiments Specific Considerations for Statistical Simulation Summary and Computing Resources Assessing Variability in Univariate Samples: Sectioning, Jackknifing, and Bootstrapping Introduction Preliminaries Assessing Variability of Sample Means and Percentiles Sectioning to Assess Variability: Arbitrary Estimates from Non-Normal Samples Bias Elimination Variance Assessment with the Complete Jackknife Variance Assessment with the Bootstrap Simulation Studies of Confidence Interval Estimation Schemes Bivariate Random Variables: Definitions, Generation, and Graphical Analysis Introduction Specification and Properties of Bivariate Random Variables Numerical and Graphical Analyses for Bivariate Data The Bivariate Inverse Probability Integral Transform Ad Hoc and Model-Based Methods for Bivariate Random Variable Generation Variance Reduction Introduction Antithetic Variates: Induced Negative Correlation Control Variables Conditional Sampling Importance Sampling Stratified Sampling