{"product_id":"on-the-distribution-of-a-glenn-walker-9780530007175","title":"On the Distribution of a Linear Combination of T-distributed Variables","description":"Abstract: \u003cp\u003e\u003c\/p\u003eFor 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. \u003cp\u003e\u003c\/p\u003eIf 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 \u0026gt; 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. \u003cp\u003e\u003c\/p\u003eDissertation 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.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Glenn Walker\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 0530007177\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9780530007175\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Dissertation Discovery Company\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/31\/2019\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 118\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.25lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.50w x 0.31d","brand":"Glenn Walker","offers":[{"title":"Hardcover","offer_id":48112923672831,"sku":"9780530007175","price":93.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_b39799fa-0522-4e4e-af1f-7e0cd43a2ea3.jpg?v=1769611861","url":"https:\/\/www.whiterainbookhouse.com\/products\/on-the-distribution-of-a-glenn-walker-9780530007175","provider":"WR Book House","version":"1.0","type":"link"}