Probability and Statistical Inference

Nitis Mukhopadhyay

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English

CRC Press
30 September 2020

Mathematics

Series: Statistics: A Series of Textbooks and Monographs

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.

By: Nitis Mukhopadhyay
Imprint: CRC Press
Country of Publication: United Kingdom
Dimensions: Height: 229mm, Width: 152mm,
Weight: 907g
ISBN: 9780367659493
ISBN 10: 0367659492
Series: Statistics: A Series of Textbooks and Monographs
Pages: 665
Publication Date: 30 September 2020
Audience: College/higher education , Primary
Format: Paperback
Publisher's Status: Active

Notions of probability; expectations of functions of random variables; multivariate random variables; transformations and sampling distributions; notions of stochastic convergence; sufficiency, completeness and ancillarity; point estimation; tests of hypotheses; confidence interval estimation; Bayesian methods; likelihood ratio and other tests; large-sample inference; sample size determination - two-stage procedures. Appendices: abbreviations and notation; celebration of statistics - selected biographical notes; selected statistical tables.

Nitis Mukhopadhyay

Reviews for Probability and Statistical Inference

...the book contains unique features throughout. Examples are the moment problem, which is clarified through a nice example, the role of the probability generating functions, and the central limit theorem for the sample variance. Techniques and concepts are typically illustrated through a series of examples. Within a box is routinely summarized what it is that has been accomplished or where to go from that point. At the end of each chapter a long list of exercises is arranged according the sections. ---Zentralblatt fur Mathematik, 2000 ...a marvelous book for students. -Statistical Papers ...a handy reference as well as a good textbook. -International Statistical Institute, Short Book Reviews

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Probability and Statistical Inference

Nitis Mukhopadhyay

$96.99

Paperback

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