On the Distribution of a Linear Combination of T-distributed Variables, Walker Glenn

Автор: Walker Glenn
Название: On the Distribution of a Linear Combination of T-distributed Variables
ISBN: 0530007169 ISBN-13(EAN): 9780530007168
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Описание: Abstract:

For odd degrees of freedom the characteristic function of a Student-t random variable is expressible in closed form. The characteristic function of an arbitrary linear combination of independent t-variables is then derived and the distribution function is obtained, itself expressible as a weighted sum of Student-t distribution functions. An easy method of obtaining the weights is demonstrated.

If U1, U1, ..., Un are independent random variables and Xi = d + Ui, i=1,2, ..., n are observable random variables, we investigate the choice of a1, a2, ..., an to maximize the power of tests of the form a1X1 + a2X2 + ... + anXn for testing Ho: d = 0 against H1: d > 0. Some general results and examples are given. Of particular interest is the case when Xi is a t-random variable. One application is in a two-stage sampling procedure to solve the Behrens-Fisher problem. The test statistic has the distribution of a weighted sum of t-random variables. It is shown how to choose the weights for maximum power.

Dissertation Discovery Company and University of Florida are dedicated to making scholarly works more discoverable and accessible throughout the world. This dissertation, "On the Distribution of a Linear Combination of T-distributed Variables" by Glenn Alan Walker, was obtained from University of Florida and is being sold with permission from the author. A digital copy of this work may also be found in the university's institutional repository, IR@UF. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation.

Автор: Walker Glenn a., Shostak Jack
Название: Common Statistical Methods for Clinical Research with SAS Examples, Third Edition
ISBN: 1642953083 ISBN-13(EAN): 9781642953084
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Описание: Glenn Walker and Jack Shostak's Common Statistical Methods for Clinical Research with SAS Examples, Third Edition, is a thoroughly updated edition of the popular introductory statistics book for clinical researchers. This new edition has been extensively updated to include the use of ODS graphics in numerous examples as well as a new emphasis on PROC MIXED. Straightforward and easy to use as either a text or a reference, the book is full of practical examples from clinical research to illustrate both statistical and SAS methodology. Each example is worked out completely, step by step, from the raw data.

Common Statistical Methods for Clinical Research with SAS Examples, Third Edition, is an applications book with minimal theory. Each section begins with an overview helpful to nonstatisticians and then drills down into details that will be valuable to statistical analysts and programmers. Further details, as well as bonus information and a guide to further reading, are presented in the extensive appendices. This text is a one-source guide for statisticians that documents the use of the tests used most often in clinical research, with assumptions, details, and some tricks--all in one place.