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 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