统计模拟

作者简介

统计模拟（英文版·第3版），ISBN：9787115141255，作者：（美）罗斯 著

书籍目录

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

内容概要

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。

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