The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods.

Author: N. Balakrishnan

Publisher: Academic Press

ISBN: 9780123977830

Category: Mathematics

Page: 256

View: 479

Chi-Squared Goodness of Fit Tests with Applications provides a thorough and complete context for the theoretical basis and implementation of Pearson’s monumental contribution and its wide applicability for chi-squared goodness of fit tests. The book is ideal for researchers and scientists conducting statistical analysis in processing of experimental data as well as to students and practitioners with a good mathematical background who use statistical methods. The historical context, especially Chapter 7, provides great insight into importance of this subject with an authoritative author team. This reference includes the most recent application developments in using these methods and models. Systematic presentation with interesting historical context and coverage of the fundamentals of the subject Presents modern model validity methods, graphical techniques, and computer-intensive methods Recent research and a variety of open problems Interesting real-life examples for practitioners

It surveysthe leading methods of testing fit . .. provides tables to make the tests available . .. assessesthe comparative merits of different test procedures . .. and supplies numerical examples to aidin understanding these techniques ...

Author: Ralph B. D'Agostino

Publisher: CRC Press

ISBN: 0824774876

Category: Mathematics

Page: 576

View: 818

Conveniently grouping methods by techniques, such as chi-squared and empirical distributionfunction, and also collecting methods of testing for specific famous distributions, this useful reference is the first comprehensive review of the extensive literature on the subject. It surveysthe leading methods of testing fit . .. provides tables to make the tests available . .. assessesthe comparative merits of different test procedures . .. and supplies numerical examples to aidin understanding these techniques.Goodness-of-Fit Techniques shows how to apply the techniques . .. emphasizes testing for thethree major distributions, normal, exponential, and uniform . .. discusses the handling of censoreddata .. . and contains over 650 bibliographic citations that cover the field.Illustrated with tables and drawings, this volume is an ideal reference for mathematical andapplied statisticians, and biostatisticians; professionals in applied science fields, including psychologists, biometricians, physicians, and quality control and reliability engineers; advancedundergraduate- and graduate-level courses on goodness-of-fit techniques; and professional seminarsand symposia on applied statistics, quality control, and reliability.

Extensive tables of goodness-of-fit critical values for the two- and three-
parameter Weibull distributions are developed through simulation for the
Kolmogorov-Smirnov statistic, the Anderson-Darling statistic, and Shapiro-Wilk-
type correlation ...

Asymptotic theory of certain ' goodness - of - fit ' criteria based on stochastic
processes . Ann . Math . Statist . 23 193–212 . [ 2 ] BIRNBAUM , Z. W. ( 1953 ) .
On the power of a one sided test of fit for continuous probability functions . Ann .
Math .

Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic
Processes. Annals of Mathematical Statistics 23: 193–212 (1952). D. G.
Chapman. A Comparative Study of Several One-Sided Goodness of Fit Tests.
Annals of ...

Author: D. A. Monheit

Publisher:

ISBN: UOM:39015095208610

Category: Goodness-of-fit tests

Page: 33

View: 739

The concept of the ordinary probability integral transformation for use with distributions of N random variables is extended. This transformation makes possible the evaluation of fit of N-variable distributions to observational data by employing any appropriate 1-variable statistic. In evaluating a model for goodness of fit, statements as to the probability of wrongly accepting a false hypothesis must be discounted, but stated probabilities for wrongly rejecting a true hypothesis are to be taken at face value. The models considered must be of the continuous type and satisfy certain regularity conditions. The transformation is most profitably employed when inadequate sample size precludes use of total information procedures such as the chi-square test with compact multidimensional domain classes. When the available sample size is inadequate to describe an N-variable distribution yet adequate to describe a distribution of one variable then the proposed method is superior to any total information procedure. (Author).

7 W 60 55 o THE ASYMPTOTIC POWER OF THE KOLMOGOROW TESTs --- o
OF GOODNESS OF FIT * by Dana Quade December, 1959 Contract No. AF log(
658)-261 The asymptotic power of the one-sided and two-sided Kolmogorov tests
...

This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics.

Author: Timothy R.C. Read

Publisher: Springer Science & Business Media

ISBN: 9781461245780

Category: Mathematics

Page: 212

View: 144

The statistical analysis of discrete multivariate data has received a great deal of attention in the statistics literature over the past two decades. The develop ment ofappropriate models is the common theme of books such as Cox (1970), Haberman (1974, 1978, 1979), Bishop et al. (1975), Gokhale and Kullback (1978), Upton (1978), Fienberg (1980), Plackett (1981), Agresti (1984), Goodman (1984), and Freeman (1987). The objective of our book differs from those listed above. Rather than concentrating on model building, our intention is to describe and assess the goodness-of-fit statistics used in the model verification part of the inference process. Those books that emphasize model development tend to assume that the model can be tested with one of the traditional goodness-of-fit tests 2 2 (e.g., Pearson's X or the loglikelihood ratio G ) using a chi-squared critical value. However, it is well known that this can give a poor approximation in many circumstances. This book provides the reader with a unified analysis of the traditional goodness-of-fit tests, describing their behavior and relative merits as well as introducing some new test statistics. The power-divergence family of statistics (Cressie and Read, 1984) is used to link the traditional test statistics through a single real-valued parameter, and provides a way to consolidate and extend the current fragmented literature. As a by-product of our analysis, a new 2 2 statistic emerges "between" Pearson's X and the loglikelihood ratio G that has some valuable properties.

Studies. As expected, these four groups of children showed a great variety of chil
~ dren with a goodness of fit, who had the ability to cope successfully with the
stresses and expectations of their environment. Some of them, especially those
with ...

Author: Stella Chess

Publisher: Routledge

ISBN: 9781135825003

Category: Psychology

Page: 246

View: 884

First published in 1999. Routledge is an imprint of Taylor & Francis, an informa company.

The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed.

Author:

Publisher:

ISBN: OCLC:1051367391

Category:

Page:

View: 186

Abstract : A robust alternative to the goodness of fit is derived, aGoFs, and a systematic error in the experimental s.u.'s is found with the help of the aGoFs, which effectively veils the presence of other systematic errors. Abstract : An alternative measure to the goodness of fit (GoF) is developed and applied to experimental data. The alternative goodness of fit squared (aGoFs) demonstrates that the GoF regularly fails to provide evidence for the presence of systematic errors, because certain requirements are not met. These requirements are briefly discussed. It is shown that in many experimental data sets a correlation between the squared residuals and the variance of observed intensities exists. These correlations corrupt the GoF and lead to artificially reduced values in the GoF and in the numerical value of the wR ( F 2 ). Remaining systematic errors in the data sets are veiled by this mechanism. In data sets where these correlations do not appear for the entire data set, they often appear for the decile of largest variances of observed intensities. Additionally, statistical errors for the squared goodness of fit, GoFs, and the aGoFs are developed and applied to experimental data. This measure shows how significantly the GoFs and aGoFs deviate from the ideal value one.

Carol E. Marchetti and Govind S. Mudholkar Rochester Institute of Technology,
Rochester, New York University of Rochester, Rochester, New York Abstract: Karl
Pearson's chi-square goodness-of-fit test of 1900 is considered an epochal ...

Author: C. Huber-Carol

Publisher: Springer Science & Business Media

ISBN: 0817642099

Category: Computers

Page: 507

View: 825

The 37 expository articles in this volume provide broad coverage of important topics relating to the theory, methods, and applications of goodness-of-fit tests and model validity. The book is divided into eight parts, each of which presents topics written by expert researchers in their areas. Key features include: * state-of-the-art exposition of modern model validity methods, graphical techniques, and computer-intensive methods * systematic presentation with sufficient history and coverage of the fundamentals of the subject * exposure to recent research and a variety of open problems * many interesting real life examples for practitioners * extensive bibliography, with special emphasis on recent literature * subject index This comprehensive reference work will serve the statistical and applied mathematics communities as well as practitioners in the field.

The testing of the hypothesis that the random process follows a specific
theoretical probability distribution is the primary function to a " goodness of fit "
test . " Goodness of fit " testing is accomplished by collecting data by observation
of the ...

tact Steve di Schwagen Abstract Goodness - of - fit tests for normality are
important because many statises assume an 10ru tical procedures assume an
underlying normal distribution , and application of these procedures without
examining ...

has been treated by H . CRAMÉR who suggested ' a special criterion and applied
it systematically to test the goodness of fit of the CHARLIER series . Later on the
same criterion was advanced by R . v . Mises ? who seemed to be unaware of ...

generalization of a procedure suggested by Weiss [ 39 ] for sequentially testing
the simple goodness - of - fit hypothesis wherein both the form and the
parameters of the hypothesized distribution are completely specified . Following
Weiss ...

Author: Christopher Stroude WithersPublish On: 1970

[ 3 ] Anderson , T . W . and Darling , D . A . ( 1952 ) , Asymptotic theory of certain ' goodness of fit ' criteria based on stochastic processes , AMS , 23 , 193 - 212 . [ 4
] Anscombe , F . J . ( 1963 ) , Tests of goodness of fit , JRSS , B25 , 81 - 94 .

Author: Christopher Stroude Withers

Publisher:

ISBN: STANFORD:36105025643508

Category: Asymptotic expansions

Page: 256

View: 784

The paper synthesizes ideas of Hoadley, Abrahamson, Bahadur, Chernoff, Hodges and Lehmann, and others with the methods of the calculus of variations, and differential and integral equations, in order to develop the theory of, and compute the efficiencies of, a wide range of goodness-of-fit tests when the underlying distribution is continuous and univariate. Also generalized are ideas of Hajek, Anderson, and Darling to find the power of some goodness-of-fit tests. (Author).

APPROXIMATE METHODS FOR CALCULATING THE POWER OF CERTAIN GOODNESS - OF - FIT TESTS In this paper two methods for calculating the
power of certain goodness - of - fit tests will be developed . This approach will be
valid in ...

Goodness of fit is concerned with assessing the validity of models involving
statistical distributions, an essential and sometimes forgotten aspect of the
modeling exercise. One can only speculate on how many wrong decisions are
made due to ...

Author: J. C. W. Rayner

Publisher: John Wiley & Sons

ISBN: 9780470824436

Category: Mathematics

Page: 320

View: 228

In this fully revised and expanded edition of Smooth Tests of Goodness of Fit, the latest powerful techniques for assessing statistical and probabilistic models using this proven class of procedures are presented in a practical and easily accessible manner. Emphasis is placed on modern developments such as data-driven tests, diagnostic properties, and model selection techniques. Applicable to most statistical distributions, the methodology described in this book is optimal for deriving tests of fit for new distributions and complex probabilistic models, and is a standard against which new procedures should be compared. New features of the second edition include: Expansion of the methodology to cover virtually any statistical distribution, including exponential families Discussion and application of data-driven smooth tests Techniques for the selection of the best model for the data, with a guide to acceptable alternatives Numerous new, revised, and expanded examples, generated using R code Smooth Tests of Goodness of Fit is an invaluable resource for all methodological researchers as well as graduate students undertaking goodness-of-fit, statistical, and probabilistic model assessment courses. Practitioners wishing to make an informed choice of goodness-of-fit test will also find this book an indispensible guide. Reviews of the first edition: "This book gives a very readable account of the smooth tests of goodness of fit. The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; research will find it helpful for the further development of smooth tests." --T.K. Chandra, Zentralblatt für Mathematik und ihre Grenzgebiete, Band 73, 1/92' "An excellent job of showing how smooth tests (a class of goodness of fit tests) are generally and easily applicable in assessing the validity of models involving statistical distributions....Highly recommended for undergraduate and graduate libraries." --Choice "The book can be read by scientists having only an introductory knowledge of statistics. It contains a fairly extensive list of references; researchers will find it helpful for the further development of smooth tests."--Mathematical Reviews "Very rich in examples . . . Should find its way to the desks of many statisticians." --Technometrics