统计模拟
2006-1
人民邮电出版社
(美)Sheldon M.Ro
274
382000
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本书介绍了统计模拟的一些实用方法和技术。在对概率的基本知识进行了简单的回顾这后，介绍了如何利用计算机产生随机数以及如何利用这些随机数产生任意分布的随机变量、随机过程等。然后介绍一些分析编译数据的方法和技术，如Bootstrap、方差缩减技术等。接着介绍了如何利用统计模拟来判断所选的随机模型是否拟合实际的数据。最后介绍了MCMC及一些最新发展的统计模拟技术和论题。 本书可作为统计学、计算数学、保险学、精算学等专业本科生教材，也可供相关专业人士参考。
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 ReferencesIndex
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