The Moments of the Non-central T-distribution PDF Download

Author: David Hogben
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 42

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Book Description

Author: Mohammad Ahsanullah
Publisher: Springer Science & Business Media
ISBN: 9462390614
Category : Mathematics
Languages : en
Pages : 163

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Book Description
The most important properties of normal and Student t-distributions are presented. A number of applications of these properties are demonstrated. New related results dealing with the distributions of the sum, product and ratio of the independent normal and Student distributions are presented. The materials will be useful to the advanced undergraduate and graduate students and practitioners in the various fields of science and engineering.

Author:
Publisher:
ISBN:
Category : Weights and measures
Languages : en
Pages : 574

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Book Description

Author: Marco Taboga
Publisher: Createspace Independent Publishing Platform
ISBN: 9781981369195
Category : Mathematical statistics
Languages : en
Pages : 670

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Book Description
The book is a collection of 80 short and self-contained lectures covering most of the topics that are usually taught in intermediate courses in probability theory and mathematical statistics. There are hundreds of examples, solved exercises and detailed derivations of important results. The step-by-step approach makes the book easy to understand and ideal for self-study. One of the main aims of the book is to be a time saver: it contains several results and proofs, especially on probability distributions, that are hard to find in standard references and are scattered here and there in more specialistic books. The topics covered by the book are as follows. PART 1 - MATHEMATICAL TOOLS: set theory, permutations, combinations, partitions, sequences and limits, review of differentiation and integration rules, the Gamma and Beta functions. PART 2 - FUNDAMENTALS OF PROBABILITY: events, probability, independence, conditional probability, Bayes' rule, random variables and random vectors, expected value, variance, covariance, correlation, covariance matrix, conditional distributions and conditional expectation, independent variables, indicator functions. PART 3 - ADDITIONAL TOPICS IN PROBABILITY THEORY: probabilistic inequalities, construction of probability distributions, transformations of probability distributions, moments and cross-moments, moment generating functions, characteristic functions. PART 4 - PROBABILITY DISTRIBUTIONS: Bernoulli, binomial, Poisson, uniform, exponential, normal, Chi-square, Gamma, Student's t, F, multinomial, multivariate normal, multivariate Student's t, Wishart. PART 5 - MORE DETAILS ABOUT THE NORMAL DISTRIBUTION: linear combinations, quadratic forms, partitions. PART 6 - ASYMPTOTIC THEORY: sequences of random vectors and random variables, pointwise convergence, almost sure convergence, convergence in probability, mean-square convergence, convergence in distribution, relations between modes of convergence, Laws of Large Numbers, Central Limit Theorems, Continuous Mapping Theorem, Slutsky's Theorem. PART 7 - FUNDAMENTALS OF STATISTICS: statistical inference, point estimation, set estimation, hypothesis testing, statistical inferences about the mean, statistical inferences about the variance.

Author: Stanford University. Applied Mathematics and Statistics Laboratory
Publisher:
ISBN:
Category : t-test (Statistics)
Languages : en
Pages : 41

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Book Description
The technical report presents a table of the percentage points of the non-central t-distribution. Denote the degrees of freedom of the non-central t-distribution by f and the non-centrality parameter by delta. The percentage points, t sub o (f, delta, epsilon), are tabulated as a function of Delta = delta /square root(f) = 0.0 (.1) 3.5, f = 4 (1) 10, 12, 18, 24, 36, 48, and probability levels epsilon = .001, .005, .010, .025, .050 (.05) .250, .500, .750, .800 (.05) .950, .975, .990, .995. This work enables the direct calculation of t sub o (f, delta, epsilon) and facilitates the computation of delta (f, t, epsilon), and covers a wider range of epsilon and delta than any other existing table except for the Johnson and Welch approximation method. Among its many uses is getting a confidence bound on the population of a normal distribution, with unknown parameters falling below (above) a preassigned limit, and solving other problems in sampling inspection by variables. (Author).

Author: K. Krishnamoorthy
Publisher: CRC Press
ISBN: 1420011375
Category : Mathematics
Languages : en
Pages : 371

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Book Description
In the area of applied statistics, scientists use statistical distributions to model a wide range of practical problems, from modeling the size grade distribution of onions to modeling global positioning data. To apply these probability models successfully, practitioners and researchers must have a thorough understanding of the theory as well as a

Author: Aerospace Research Laboratories (U.S.)
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 488

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Book Description

Author: Norman L. Johnson
Publisher: John Wiley & Sons
ISBN: 0471584940
Category : Mathematics
Languages : en
Pages : 747

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Book Description
Comprehensive reference for statistical distributions Continuous Univariate Distributions, Volume 2 provides in-depth reference for anyone who applies statistical distributions in fields including engineering, business, economics, and the sciences. Covering a range of distributions, both common and uncommon, this book includes guidance toward extreme value, logistics, Laplace, beta, rectangular, noncentral distributions and more. Each distribution is presented individually for ease of reference, with clear explanations of methods of inference, tolerance limits, applications, characterizations, and other important aspects, including reference to other related distributions.

Author: David Hogben
Publisher:
ISBN:
Category : Calculus of variations
Languages : en
Pages : 52

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Book Description

Author: WIlliam J. Kennedy
Publisher: Routledge
ISBN: 1351414585
Category : Mathematics
Languages : en
Pages : 360

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Book Description
In this book the authors have assembled the "best techniques from a great variety of sources, establishing a benchmark for the field of statistical computing." ---Mathematics of Computation ." The text is highly readable and well illustrated with examples. The reader who intends to take a hand in designing his own regression and multivariate packages will find a storehouse of information and a valuable resource in the field of statistical computing.