Automatic Nonuniform Random Variate Generation

Cover
Title page
Preface
Part 1 Preliminaries
1 Introduction
2 General Principles in Random Variate Generation
2.1 The Inversion Method
2.2 The Rejection Method
2.3 Composition
2.4 The Ratio-of- Uniforms Method (RoU)
2.5 Almost-Exact Inversion
2.6 Using Special Properties of the Distribution
2.7 Exercises
3 General Principles for Discrete Distributions
3.1 Inversion
3.2 The Alias Method
3.3 Discrete Rejection
3.4 Exercises
Part II Continuous Univariate Distributions
4 Transformed Density Rejection (TDR)
4.1 The Main Idea
4.2 The Class T_c of Transformations
4.3 T_c-Concave Distributions
4.4 Construction Points
4.5 Aigorithms and Variants of Transformed Density Rejection
4.6 Other Transformations
4.7 Generalizations of Transformed Density Rejection
4.8 Automatic Ratio-of-Uniforms Method
4.9 Exercises
5 Strip Methods
5.1 Staircase-Shaped Hat Functions ("Ahrens Method")
5.2 Horizontal Strips
5.3 Exercises
6 Methods Based on General Inequalities
6.1 Monotone Densities
6.2 Lipschitz Densities
6.3 Generators for T_{-1/2}-Concave Densities
6.4 Generators for T_c-Concave Densities
6.5 Exercises
7 Numerical Inversion
7.1 Search Algorithms Without Tables
7.2 Fast Numerical Inversion
7.3 Exercises
8 Comparison and General Considerations
8.1 The UNU.RAN Library
8.2 Timing Results
8.3 Quality of Generated Samples
8.4 Special Applications
8.5 Summary
9 Distributions Where the Density Is Not Known Explicitly
9.1 Known Hazard-Rate
9.2 The Series Method
9.3 Known Fourier Coefficients
9.4 Known Characteristic Function
9.5 Exercises
Part III Discrete Univariate Distributions
10 Discrete Distributions
10.1 Guide Table Method for Unbounded Domains
10.2 Transformed Probability Rejection (TPR)
10.3 Short Algorithms Based on General Inequalities
10.4 Distributions Where the Probabilities Are Not Known Explicitly
10.5 Computational Experience
10.6 Summary
10.7 Exercises
Part IV Random Vectors
11 Multivariate Distributions
11.1 General Principles for Generating Random Vectors
11.2 Uniformly Distributed Random Vectors
11.3 Multivariate Transformed Density Rejection
11.4 Orthomonotone Densities
11.5 Computational Experience
11.6 Multivariate Discrete Distributions
11.7 Exercises
Part V Implicit Modeling
12 Combination of Generation and Modeling
12.1 Generalizing a Sample
12.2 Generalizing a Vector-Sample
12.3 Modeling of Distributions with Limited Information
12.4 Distribution with Known Moments
12.5 Generation of Random Vectors where only Correlation and Marginal Distributions are Known
12.6 Exercises
13 Time Series (Authors Michael Hauser and Wolfgang Hörmann)
13.1 Stationary Gaussian Time Series
13.2 Non-Gaussian Time Series
13.3 Exercises
14 Markov Chain Monte Carlo Methods
14.1 Markov Chain Sampling Aigorithms
14.2 Perfect Sampling for Markov Chain Monte Carlo
14.3 Markov Chain Monte Carlo Methods for Random Vectors
14.4 Exercises
15 Some Simulation Examples
15.1 Financial Simulation
15.2 Bayesian Statistics
15.3 Exercises
List of Algorithms
References
Author index