Download or read book Goodness of fit Tests for Testing Multivariate Families of Distributions written by Nabil Ali Ahmed and published by . This book was released on 1987 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Goodness of Fit Statistics for Discrete Multivariate Data written by Timothy R.C. Read and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Smooth Tests of Goodness of Fit written by J. C. W. Rayner and published by John Wiley & Sons. This book was released on 2009-07-23 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book The Improvement of Testing Procedures for Chi Square Goodness of Fit Tests written by David S. Moore and published by . This book was released on 1973 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The research concentrated on large-sample properties of chi-squared tests of fit for multivariate families of distributions. Both Bahadur and Pitman approaches to large-sample power were pursued, with substantial results in each case. (Modified author abstract).
Download or read book Smooth Tests of Goodness of Fit written by J. C. W. Rayner and published by Oxford University Press, USA. This book was released on 1989 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Goodness of fit describes the validity of models involving statistical distributions of data, and smooth tests are a subset of these tests that can be used in any situation in which there are relatively large sample sizes.
Download or read book Properties of a Multivariate Goodness of Fit Test written by Toke Jayachandran and published by . This book was released on 1982 with total page 22 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an earlier paper the authors compared the Foutz test with the Chi-square and Kolmogorov-Smirnov test. The results indicated that the Foutz test is more powerful in detecting certain characteristics than the other two tests. This paper deals with the performance of the test when fitting multivariate distributions. More specifically the power of the test when fitting bivariate and trivariate normal distributions for various choices of the mean vector and the covariance matrix is investigated. In the second section is presented a brief description of the Foutz test; a discussion of the simulation procedure is in the third section and the results of the simulation are in the final section.
Download or read book Construction of Conditional Statistics for Chi square Goodness of Fit Tests written by Charles E. McCulloch and published by . This book was released on 1980 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Properties of a Multivariate Goodness of Fit Test written by and published by . This book was released on 1982 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an earlier paper the authors compared the Foutz test with the Chi-square and Kolmogorov-Smirnov test. The results indicated that the Foutz test is more powerful in detecting certain characteristics than the other two tests. This paper deals with the performance of the test when fitting multivariate distributions. More specifically the power of the test when fitting bivariate and trivariate normal distributions for various choices of the mean vector and the covariance matrix is investigated. In the second section is presented a brief description of the Foutz test; a discussion of the simulation procedure is in the third section and the results of the simulation are in the final section.
Download or read book Goodness of Fit Tests and Model Validity written by C. Huber-Carol and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Chi Squared Goodness of Fit Tests with Applications written by Narayanaswamy Balakrishnan and published by Academic Press. This book was released on 2013-01-25 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Copulae and Multivariate Probability Distributions in Finance written by Alexandra Dias and published by Routledge. This book was released on 2013-08-21 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: Portfolio theory and much of asset pricing, as well as many empirical applications, depend on the use of multivariate probability distributions to describe asset returns. Traditionally, this has meant the multivariate normal (or Gaussian) distribution. More recently, theoretical and empirical work in financial economics has employed the multivariate Student (and other) distributions which are members of the elliptically symmetric class. There is also a growing body of work which is based on skew-elliptical distributions. These probability models all exhibit the property that the marginal distributions differ only by location and scale parameters or are restrictive in other respects. Very often, such models are not supported by the empirical evidence that the marginal distributions of asset returns can differ markedly. Copula theory is a branch of statistics which provides powerful methods to overcome these shortcomings. This book provides a synthesis of the latest research in the area of copulae as applied to finance and related subjects such as insurance. Multivariate non-Gaussian dependence is a fact of life for many problems in financial econometrics. This book describes the state of the art in tools required to deal with these observed features of financial data. This book was originally published as a special issue of the European Journal of Finance.
Download or read book A Bivariate Test of Goodness of Fit Based on a Gradually Increasing Number of Order Statistics written by José Kreimerman and published by . This book was released on 1975 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: An important area of Statistical Inference relates to the problem of assessing the conformity or goodness of fit of some observations to a null hypothesis. This hypothesis may be that the observations came from a distribution which belongs to a given family or may be a completely specified distribution. A statistical procedure which solves such a problem is called a test of goodness of fit. This thesis is concerned with the problem of testing the goodness of fit of a sample drawn from a continuous bivariate distribution, where the null hypothesis is that the true distribution is a completely specified one. A test is developed, where the test criterion is based in some functions of a subset of order statistics, functions which depend on the distribution under the null hypothesis.
Download or read book The Frailty Model written by Luc Duchateau and published by Springer Science & Business Media. This book was released on 2007-10-23 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: Readers will find in the pages of this book a treatment of the statistical analysis of clustered survival data. Such data are encountered in many scientific disciplines including human and veterinary medicine, biology, epidemiology, public health and demography. A typical example is the time to death in cancer patients, with patients clustered in hospitals. Frailty models provide a powerful tool to analyze clustered survival data. In this book different methods based on the frailty model are described and it is demonstrated how they can be used to analyze clustered survival data. All programs used for these examples are available on the Springer website.
Download or read book Two and Three parameter Weibull Goodness of fit Tests written by James W. Evans and published by . This book was released on 1989 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Chi square Test of Goodness of Fit for a Multivariate Normal Distribution written by Carl B. Bates and published by . This book was released on 1967 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Pearson Chi-Square Goodness of Fit Criterion for testing the null hypothesis 'The random sample is from a univariate normal parent population' is generalized for multivariate normal distributions to test the null hypothesis 'The random sample of N-dimensional observation vectors is from an N-dimensional multivariate normal parent population.' The basis of the formulation is the distribution of the quadratic form in the exponent of the hypothesized distribution. Application of the procedure is illustrated with a numerical example of experimental data from a weapon effectiveness study. (Author).
Download or read book Chi squared Goodness of fit Tests for Censored Data written by Mikhail S. Nikulin and published by John Wiley & Sons. This book was released on 2017-08-07 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the problems of construction and application of chi-squared goodness-of-fit tests for complete and censored data. Classical chi-squared tests assume that unknown distribution parameters are estimated using grouped data, but in practice this assumption is often forgotten. In this book, we consider modified chi-squared tests, which do not suffer from such a drawback. The authors provide examples of chi-squared tests for various distributions widely used in practice, and also consider chi-squared tests for the parametric proportional hazards model and accelerated failure time model, which are widely used in reliability and survival analysis. Particular attention is paid to the choice of grouping intervals and simulations. This book covers recent innovations in the field as well as important results previously only published in Russian. Chi-squared tests are compared with other goodness-of-fit tests (such as the Cramer-von Mises-Smirnov, Anderson-Darling and Zhang tests) in terms of power when testing close competing hypotheses.
Download or read book Statistical Inference Based on Divergence Measures written by Leandro Pardo and published by CRC Press. This book was released on 2018-11-12 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of using functionals of Information Theory, such as entropies or divergences, in statistical inference is not new. However, in spite of the fact that divergence statistics have become a very good alternative to the classical likelihood ratio test and the Pearson-type statistic in discrete models, many statisticians remain unaware of this p
