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Full Description
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.
Contents
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
