| “……本书内容丰富，不论作为教材还是参考书都非常值得推荐。” ——美国统计学报 “本书是一本非常优秀的教材，强调了计算机在模拟技术上的应用。一定的概率和统计知识将有助于理解本书的精髓。” ——亚马逊网上书店评论 统计模拟是一门新兴的统计学和计算机结合的学科，因其便利性和经济性而广泛应用于统计学、数学、精算科学、工程学、物理学等众多领域，用以获得精确而有效的解决方案。 本书是国际知名统计学家Sheldon M. Ross所著的经典教材，已被加州大学伯克利分校、哥伦比亚大学等多所名校采用。书中涵盖了统计模拟最新方法和技术，提供了丰富的实例，备受业界推崇。 本书特色： 提供了分析模拟数据以及模拟模型的拟合检验所需的统计方法。 通过许多实用的例子（如多服务器排队法、存货控制及行使股票期权等）来阐明和提出理论。 强调方差缩减技术，包括控制变量及它们在因归分析中的应用等。 单列一单介绍Markov Chain Monte Carlo方法。 提供了关于产生离散随机变量混淆方法的独特材料。 新增加了有关保险风险模型、生成随机向量及奇异期权的材料。 |
| Sheldon M.Ross国际知名统计学家，加州大学伯克利分校工业工程与运筹系教授。毕业于斯坦福大学统计系。研究领域包括：随机模型、仿真模拟、统计分析及金融数学等。除本书外，Ross教授还是多本畅销数学和统计教材的作者。 |
| 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 Chebyshev's 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 |
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