統(tǒng)計模擬

內(nèi)容概要

本書介紹了統(tǒng)計模擬的一些實用方法和技術(shù)。在對概率的基本知識進(jìn)行了簡單的回顧這后，介紹了如何利用計算機產(chǎn)生隨機數(shù)以及如何利用這些隨機數(shù)產(chǎn)生任意分布的隨機變量、隨機過程等。然后介紹一些分析編譯數(shù)據(jù)的方法和技術(shù)，如Bootstrap、方差縮減技術(shù)等。接著介紹了如何利用統(tǒng)計模擬來判斷所選的隨機模型是否擬合實際的數(shù)據(jù)。最后介紹了MCMC及一些最新發(fā)展的統(tǒng)計模擬技術(shù)和論題。    本書可作為統(tǒng)計學(xué)、計算數(shù)學(xué)、保險學(xué)、精算學(xué)等專業(yè)本科生教材，也可供相關(guān)專業(yè)人士參考。

作者簡介

Sheldon M.Ross國際知名統(tǒng)計學(xué)家，加州大學(xué)伯克利分校工業(yè)工程與運籌系教授。畢業(yè)于斯坦福大學(xué)統(tǒng)計系。研究領(lǐng)域包括：隨機模型、仿真模擬、統(tǒng)計分析及金融數(shù)學(xué)等。除本書外，Ross教授還是多本暢銷數(shù)學(xué)和統(tǒng)計教材的作者。

書籍目錄

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

圖書封面

圖書標(biāo)簽Tags

無

評論、評分、閱讀與下載

---

    統(tǒng)計模擬 PDF格式下載

---