Nitis Mukhopadhyay – Probability and Statistical Inference

Nitis Mukhopadhyay – Probability and Statistical Inference

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Priced very competitively compared with other textbooks at this level! This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference   studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions   develops notions of convergence in probability and distribution   spotlights the central limit theorem (CLT) for the sample variance   introduces sampling distributions and the Cornish-Fisher expansions   concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity   explains Basu’s Theorem as well as location, scale, and location-scale families of distributions   covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality   discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems   focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals   includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient   summarizes Bayesian methods   describes the monotone likelihood ratio (MLR) property   handles variance stabilizing transformations   provides a historical context for statistics and statistical discoveries   showcases great statisticians through biographical notes Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.