Sharp Inequalities for Ordered Random Variables in Statistics and Reliability

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Focusing on inequalities and bounds related to order statistics, this book provides an in-depth exploration of deterministic bounds and their applications across various statistical contexts, including IID samples from general and symmetric distributions. It also addresses shape-restricted distributions and finite populations. The text features a comprehensive numerical evaluation that compares different bounds, emphasizing their precision and inherent differences. Additionally, it highlights applications in inference, reliability theory, and characterizations, making it a valuable resource for statisticians and researchers.