Simulation – Sheldon M. Ross – 5th Edition

Description

The 5th edition of Ross’s Simulation continues to introduce aspiring and practicing actuaries; engineers; computer and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers learn to apply results of these analyses to in a wide variety of fields to obtain effective; accurate and make predictions about future outcomes.

This latest edition features all-new material on variance reduction; including control variables and their use in estimating the expected return at blackjack and their relation to analysis. Additionally; the 5th edition expands on Markov chain monte carlo methods; and offers unique information on the alias method for generating discrete random variables.

By explaining how a can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time; Ross’s Simulation; 5th edition presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.

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  • Preface
    Overview
    New to This Edition
    Chapter Descriptions
    Thanks

    Chapter 1. Introduction
    Exercises

    Chapter 2. Elements of Probability
    2.1 Sample Space and Events
    2.2 Axioms of Probability
    2.3 Conditional Probability and Independence
    2.4 Random Variables
    2.5 Expectation
    2.6 Variance
    2.7 Chebyshev’s Inequality and the Laws of Large Numbers
    2.8 Some Discrete Random Variables
    2.9 Continuous Random Variables
    2.10 Conditional Expectation and Conditional Variance
    Exercises
    References

    Chapter 3. Random Numbers
    Introduction
    3.1 Pseudorandom Number Generation
    3.2 Using Random Numbers to Evaluate Integrals
    Exercises
    References

    Chapter 4. Generating Discrete Random Variables
    4.1 The Inverse Transform Method
    4.2 Generating a Poisson Random Variable
    4.3 Generating Binomial Random Variables
    4.4 The Acceptance– Rejection Technique
    4.5 The Composition Approach
    4.6 The Alias Method for Generating Discrete Random Variables
    4.7 Generating Random Vectors
    Exercises

    Chapter 5. Generating Continuous Random Variables
    Introduction
    5.1 The Inverse Transform Algorithm
    5.2 The Rejection Method
    5.3 The Polar Method for Generating Normal Random Variables
    5.4 Generating a Poisson Process
    5.5 Generating a Nonhomogeneous Poisson Process
    5.6 Simulating a Two-Dimensional Poisson Process
    Exercises
    References

    Chapter 6. The Multivariate Normal Distribution and Copulas
    Introduction
    6.1 The Multivariate Normal
    6.2 Generating a Multivariate Normal Random Vector
    6.3 Copulas
    6.4 Generating Variables from Copula Models
    Exercises

    Chapter 7. The Discrete Event Simulation Approach
    Introduction
    7.1 Simulation via Discrete Events
    7.2 A Single-Server Queueing System
    7.3 A Queueing System with Two Servers in Series
    7.4 A Queueing System with Two Parallel Servers
    7.5 An Inventory Model
    7.6 An Insurance Risk Model
    7.7 A Repair Problem
    7.8 Exercising a Stock Option
    7.9 Verification of the Simulation Model
    Exercises
    References

    Chapter 8. Statistical Analysis of Simulated Data
    Introduction
    8.1 The Sample Mean and Sample Variance
    8.2 Interval Estimates of a Population Mean
    8.3 The Bootstrapping Technique for Estimating Mean Square Errors
    Exercises
    References

    Chapter 9. Variance Reduction Techniques
    Introduction
    9.1 The Use of Antithetic Variables
    9.2 The Use of Control Variates
    9.3 Variance Reduction by Conditioning
    9.4 Stratified Sampling
    9.5 Applications of Stratified Sampling
    9.6 Importance Sampling
    9.7 Using Common Random Numbers
    9.8 Evaluating an Exotic Option
    9.9 Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions
    Exercises
    References

    Chapter 10. Additional Variance Reduction Techniques
    Introduction
    2 The Conditional Bernoulli Sampling Method
    3 Normalized Importance Sampling
    4 Latin Hypercube Sampling
    Exercises

    Chapter 11. Statistical Validation Techniques
    Introduction
    11.1 Goodness of Fit Tests
    11.2 Goodness of Fit Tests When Some Parameters Are Unspecified
    11.3 The Two-Sample Problem
    11.4 Validating the Assumption of a Nonhomogeneous Poisson Process
    Exercises
    References

    Chapter 12. Markov Chain Monte Carlo Methods
    Introduction
    12.1 Markov Chains
    12.2 The Hastings–Metropolis Algorithm
    12.3 The Gibbs Sampler
    12.4 Continuous time Markov Chains and a QueueingLoss Model
    12.5 Simulated Annealing
    12.6 The Sampling Importance Resampling Algorithm
    12.7 Coupling from the Past
    Exercises
    References
    Index
  • Citation

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