"Non-Uniform Random Variate Generation" by Luc Devroye is a comprehensive text on the generation of random numbers with non-uniform distributions. It covers the theoretical foundations and practical algorithms for generating random variables with various distributions, including discrete and continuous ones. The book is aimed at statisticians, operations researchers, and computer scientists who need random numbers for simulations, testing, and algorithm comparisons. It discusses the complexity of random variate generation algorithms, introduces concepts like uniformly bounded expected complexity, and provides upper and lower bounds for computational complexity. The text includes detailed explanations of methods such as the inversion method, rejection method, acceptance-complement method, and decomposition as discrete mixtures. It also covers specialized algorithms like the Forsythe-von Neumann method, the series method, and the ratio-of-uniforms method. The book includes a wide range of examples and exercises, and it discusses various distributions such as normal, exponential, gamma, beta, t, and stable distributions. It also covers multivariate distributions, random combinatorial objects, and probabilistic shortcuts. The text is written in a clear and concise manner, with a focus on both theory and practice, and it is suitable for advanced students and professionals in the field of probability and statistics."Non-Uniform Random Variate Generation" by Luc Devroye is a comprehensive text on the generation of random numbers with non-uniform distributions. It covers the theoretical foundations and practical algorithms for generating random variables with various distributions, including discrete and continuous ones. The book is aimed at statisticians, operations researchers, and computer scientists who need random numbers for simulations, testing, and algorithm comparisons. It discusses the complexity of random variate generation algorithms, introduces concepts like uniformly bounded expected complexity, and provides upper and lower bounds for computational complexity. The text includes detailed explanations of methods such as the inversion method, rejection method, acceptance-complement method, and decomposition as discrete mixtures. It also covers specialized algorithms like the Forsythe-von Neumann method, the series method, and the ratio-of-uniforms method. The book includes a wide range of examples and exercises, and it discusses various distributions such as normal, exponential, gamma, beta, t, and stable distributions. It also covers multivariate distributions, random combinatorial objects, and probabilistic shortcuts. The text is written in a clear and concise manner, with a focus on both theory and practice, and it is suitable for advanced students and professionals in the field of probability and statistics.