"Probability And Statistical Inference | Statistics

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 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.|Probability and Statistical Inference | Statistics