Simulation Methodology for Statisticians, Operations Analysts, and Engineers

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