Theory and Tables for Tests of Hypotheses Concerning the Mean and the Variance of a Weibull Population
Author | : Harman Leon Harter |
Publisher | : |
Total Pages | : 210 |
Release | : 1967 |
Genre | : Statistical hypothesis testing |
ISBN | : |
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Author | : Harman Leon Harter |
Publisher | : |
Total Pages | : 210 |
Release | : 1967 |
Genre | : Statistical hypothesis testing |
ISBN | : |
Author | : Harman Leon Harter |
Publisher | : |
Total Pages | : 393 |
Release | : 1967 |
Genre | : Statistical hypothesis testing |
ISBN | : |
A summary is given of the current state of knowledge concerning the analysis of data arising from Weibull populations. Five different parameterizations which have been used by various authors are given, and the relation of the various sets of parameters to each other and to the mean and the variance is explored. It is shown that the standardized cumulants are functions only of the shape parameter. An auxiliary table is given of the mean and the variance of a Weibull population with location parameter 0 and scale parameter 1 and of the standardized cumulants gamma sub k (k = 3,4 ...,8), all for shape parameter m = 1.1(0.1)10.0. The theory is developed for tests of hypotheses concerning the mean and the variance of a Weibull population, based on the Weibull-Z, Weibull-T, and Weibull-V statistics, which are analogues of the normal-z, Student-t, and (chi square)/(degrees of freedom) statistics, respectively, the difference being that the underlying distribution is Weibull rather than normal. Percentage points of the Weibull-Z statistic are worked out by use of the Cornish-Fisher expansion technique and similar results for the Weibull-V and Weibull-T statistics are obtained by means of a Monte Carlo simulation. The percentage points are tabulated for all combinations of the above values of m; sample sizes n = 2(1)40, 48, 60, 80, 120, 240, infinity; and cumulative probabilities P = 0.005, 0.01, 0.025, 0.05, 0.1, 0.25, 0.75, 0.9, 0. 95, 0.975, 0.99, 0.995. Examples illustrating the use of the tables are given.
Author | : |
Publisher | : |
Total Pages | : 790 |
Release | : 1978 |
Genre | : Aeronautics |
ISBN | : |
Lists citations with abstracts for aerospace related reports obtained from world wide sources and announces documents that have recently been entered into the NASA Scientific and Technical Information Database.
Author | : Horst Rinne |
Publisher | : CRC Press |
Total Pages | : 812 |
Release | : 2008-11-20 |
Genre | : Business & Economics |
ISBN | : 1420087444 |
The Most Comprehensive Book on the SubjectChronicles the Development of the Weibull Distribution in Statistical Theory and Applied StatisticsExploring one of the most important distributions in statistics, The Weibull Distribution: A Handbook focuses on its origin, statistical properties, and related distributions. The book also presents various ap
Author | : Defense Documentation Center (U.S.) |
Publisher | : |
Total Pages | : 784 |
Release | : 1967 |
Genre | : Science |
ISBN | : |
Author | : United States. National Aeronautics and Space Administration. Office of Reliability and Quality Assurance |
Publisher | : |
Total Pages | : 602 |
Release | : 1968 |
Genre | : Quality control |
ISBN | : |
Author | : Lothar Sachs |
Publisher | : Springer Science & Business Media |
Total Pages | : 734 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1468401238 |
An English translation now joins the Russian and Spanish versions. It is based on the newly revised fifth edition of the German version of the book. The original edition has become very popular as a learning and reference source with easy to follow recipes and cross references for scientists in fields such as engineering, chemistry and the life sciences. Little mathematical background is required of the reader and some important topics, like the logarithm, are dealt with in the preliminaries preceding chapter one. The usefulness of the book as a reference is enhanced by a number of convenient tables and by references to other tables and methods, both in the text and in the bibliography. The English edition contains more material than the German original. I am most grateful to all who have in conversations, letters or reviews suggested improvements in or criticized earlier editions. Comments and suggestions will continue to be welcome. We are especially grateful to Mrs. Dorothy Aeppli of St. Paul, Minnesota, for providing numerous valuable comments during the preparation of the English manuscript. The author and the translator are responsible for any remaining faults and imperfections. I welcome any suggestions for improvement. My greatest personal gratitude goes to the translator, Mr. Zenon Reynaro wych, whose skills have done much to clarify the text, and to Springer-Verlag.