Probability And Statistical Inference

Description

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 Inferencestudies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributionsdevelops notions of convergence in probability and distributionspotlights the central limit theorem (CLT) for the sample varianceintroduces sampling distributions and the Cornish-Fisher expansionsconcentrates on the fundamentals of sufficiency, information, completeness, and ancillarityexplains Basu's Theorem as well as location, scale, and location-scale families of distributionscovers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequalitydiscusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theoremsfocuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervalsincludes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficientsummarizes Bayesian methodsdescribes the monotone likelihood ratio (MLR) propertyhandles variance stabilizing transformationsprovides a historical context for statistics and statistical discoveriesshowcases great statisticians through biographical notesEmploying 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.