شبیه‌سازی: ویرایش ششم

Simulation, Sixth Edition continues to introduce aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers will learn to apply the results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions. By explaining how a computer can be used to generate random numbers and how to use these random numbers to generate the behavior of a stochastic model over time, this book presents the statistics needed to analyze simulated data and validate simulation models. Includes updated content throughout Offers a wealth of practice exercises as well as applied use of free software package R Features the author's well-known, award-winning and accessible approach to complex information Front Cover Simulation Copyright Contents Preface Overview New to this edition Chapter descriptions Thanks 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 The conditional variance formula 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 Inverse transform algorithm for generating a binomial (n, p) random variable 4.4 The acceptance–rejection technique Rejection method 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 The rejection method 5.2.1 Order statistics and beta random variables 5.3 The polar method for generating normal random variables 5.4 Generating a Poisson process Generating the first T time units of a Poisson process with rate λ 5.5 Generating a nonhomogeneous Poisson process Generating the first T time units of a nonhomogeneous Poisson process Generating the first T time units of a nonhomogeneous Poisson process 5.6 Simulating a two-dimensional Poisson process Exercises References 6 The multivariate normal distribution and copulas Introduction 6.1 The multivariate normal 6.2 Generating a multivariate normal random vector 6.3 Copulas Multidimensional 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 7.9 Verification of the simulation model Exercises References 8 Statistical analysis of simulated data Introduction 8.1 The sample mean and sample variance A method for determining when to stop generating new data 8.2 Interval estimates of a population mean 8.3 The bootstrapping technique for estimating mean square errors Exercises References 9 Variance reduction techniques Introduction 9.1 The use of antithetic variables 9.2 The use of control variates 9.3 Variance reduction by conditioning 9.3.1 Estimating the expected number of renewals by time t 9.4 Stratified sampling 9.5 Applications of stratified sampling 9.5.1 Analyzing systems having Poisson arrivals 9.5.2 Computing multidimensional integrals of monotone functions 9.5.3 Compound random vectors 9.5.4 The use of post-stratification 9.6 Importance sampling 9.7 Using common random numbers 9.8 Evaluating an exotic option 9.9 Appendix: Verification of antithetic variable approach when estimating the expected value of monotone functions Exercises References 10 Additional variance reduction techniques Introduction 10.1 The conditional Bernoulli sampling method 10.2 A simulation estimator based on an identity of Chen–Stein 10.2.1 When X1, ..., Xn are independent 10.2.2 When X1, ..., Xn are dependent 10.2.3 A post-simulation estimator 10.3 Using random hazards 10.4 Normalized importance sampling 10.5 Latin hypercube sampling Exercises 11 Statistical validation techniques Introduction 11.1 Goodness of fit tests The chi-square goodness of fit test for discrete data The Kolmogorov–Smirnov test for continuous data 11.2 Goodness of fit tests when some parameters are unspecified The discrete data case The continuous data case 11.3 The two-sample problem 11.4 Validating the assumption of a nonhomogeneous Poisson process Exercises References 12 Markov chain Monte Carlo methods Introduction 12.1 Markov chains 12.2 The Hastings–Metropolis algorithm 12.3 The Gibbs sampler 12.4 Continuous time Markov chains and a queueing loss model 12.5 Simulated annealing 12.6 The sampling importance resampling algorithm 12.7 Coupling from the past Exercises References Index Back Cover