罗斯(Sheldon
M.Ross),世界著名的应用概率专家和统计学家,现为南加州大学工业与系统工程系Epstein讲座教授。他于1968年在斯坦福大学获得统计学博士学位,在1976年至2004年期间于加州大学伯克利分校任教,他的研究领域包括统计模拟、金融工程、应用概率模型、随机动态规划等。Ross教授创办了Probability
in the Engineering and lnformational
Sciences杂志并一直担任该杂志主编,他的多种畅销教材均产生了世界性的影响,其中《随机过程(第2版)》和《概率论基础教程(第9版)》等均由机械工业出版社引进出版。
目錄:
Preface
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
2.9 Continuous Random Variables
2.10 Conditional Expectation and Conditional Variance
Exercises
Bibliography
3 Random Numbers
Introduction
3.1 Pseudorandom Number Generation
3.2 Using Random Numbers to Evaluate Integrals
Exercises
Bibliography
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
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
Bibliography
6 The Multivariate Normal Distributiori 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
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
……
8 Statistical Analysis of Simulated Data
9 Variance Reduction Techniques
10 AdditionaIVoriance Reduction Techniques
11 Statistical Validation Techniques
12 Markov Chain Monte Carlo Methods
Index