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2. Random Number Generation
Pierre L'Ecuyer
Subsections
2.1 Introduction
2.2 Uniform Random Number Generators
2.2.1 Physical Devices
2.2.2 Generators Based on a Deterministic Recurrence
2.2.3 Quality Criteria
2.2.4 Statistical Testing
2.2.5 Cryptographically Strong Generators
2.3 Linear Recurrences Modulo
2.3.1 The Multiple Recursive Generator
2.3.2 The Lattice Structure
2.3.3 MRG Implementation Techniques
2.3.4 Combined MRGs and LCGs
2.3.5 Jumping Ahead
2.3.6 Linear Recurrences With Carry
2.4 Generators Based on Recurrences Modulo
2.4.1 A General Framework
2.4.2 Measures of Uniformity
2.4.3 Lattice Structure in Spaces of Polynomials and Formal Series
2.4.4 The LFSR Generator
2.4.5 The GFSR and Twisted GFSR
2.4.6 Combined Linear Generators Over
2.5 Nonlinear RNGs
2.6 Examples of Statistical Tests
2.7 Available Software and Recommendations
2.8 Non-uniform Random Variate Generation
2.8.1 Inversion
2.8.2 The Alias Method
2.8.3 Kernel Density Estimation and Generation
2.8.4 The Rejection Method
2.8.5 Thinning for Point Processes with Time-varying Rates
2.8.6 The Ratio-of-Uniforms Method
2.8.7 Composition and Convolution
2.8.8 Other Special Techniques
