統(tǒng)計模擬（英文版·第4版）

1 Introduction
Exercises
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 Chebyshevs Inequality and the Laws of Large Numbers
2.8 Some Discrete Random Variables
Binomial Random Variables
Poisson Random Variables
Geometric Random Variables
The Negative Binomial Random Variable
Hypergeometric Random Variables
2.9 Continuous Random Variables
Uniformly Distributed Random Variables
Normal Random Variables
Exponential Random Variables
The Poisson Process and Gamma Random Variables
The Nonhomogeneous Poisson Process
2.10 Conditional Expectation and Conditional Variance
Exercises
References
3 Random Numbers
Introduction
3.1 Pseudorandom Number Generation
3.2 Using Random Numbers to Evaluate Integrals
Exercises
References
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 Generating Random Vectors
Exercises
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
Exercises
References
6 The Discrete Event Simulation Approach
Introduction
6.1 Simulation via Discrete Events
6.2 A Single-Server Queueing System
6.3 A Queueing System with Two Servers in Series
6.4 A Queueing System with Two Parallel Servers
6.5 An Inventory Model
6.6 An Insurance Risk Model
6.7 A Repair Problem
6.8 Exercising a Stock Option
6.9 Verification of the Simulation Model
Exercises
References
7 Statistical Analysis of Simulated Data
Introduction
7.1 The Sample Mean and Sample Variance
7.2 Interval Estimates of a Population Mean
7.3 The Bootstrapping Technique for Estimating Mean Square Errors
Exercises
References
8 Variance Reduction Techniques
Introduction
8.1 The Use of Antithetic Variables
8.2 The Use of Control Variates
8.3 Variance Reduction by Conditioning
Estimating the Expected Number of Renewals by Time t
8.4 Stratified Sampling
8.5 Importance Sampling
8.6 Using Common Random Numbers
8.7 Evaluating an Exotic Option
Appendix： Verification of Antithetic Variable Approach
When Estimating the Expected Value of Monotone Functions
Exercises
References
9 Statistical Validation Techniques
Introduction
9.1 Goodness of Fit Tests
The Chi-Square Goodness of Fit Test for Discrete Data
The Kolmogorov-Smirnov Test for Continuous Data
9.2 Goodness of Fit Tests When Some Parameters Are Unspecified
The Discrete Data Case
The Continuous Data Case
9.3 The Two-Sample Problem
9.4 Validating the Assumption of a Nonhomogeneous
Poisson Process
Exercises
References
10 Markov Chain Monte Carlo Methods
Introduction
10.1 Markov Chains
10.2 The Hastings-Metropolis Algorithm
10.3 The Gibbs Sampler
10.4 Simulated Annealing
10.5 The Sampling Importance Resampling Algorithm
Exercises
References
11 Some Additional Topics
Introduction
11.1 The Alias Method for Generating Discrete Random Variables
11.2 Simulating a Two-Dimensional Poisson Process
11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables
11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain
11.5 Coupling from the Past
Exercises
References
Index