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Chi-squared goodness of fit tests wi...

Balakrishnan, N., (1956-)

Chi-squared goodness of fit tests with applications

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Chi-squared goodness of fit tests with applicationsV. Voinov, KIMEP University; Institute for Mathematics and Mathematical Modeling of the Ministry of Education and Science, Almaty, Kazakhstan, M. Nikulin, University Bordeaux-2, Bordeaux, France, N. Balakrishnan, McMaster University, Hamilton, Ontario, Canada.
作者:	Voinov, Vassiliy.
其他作者:	Balakrishnan, N.,
出版者:	Amsterdam :Elsevier/AP,2013.
面頁冊數:	xii, 229 p. :ill. ;24 cm.
標題:	Chi-square test.
電子資源:	http://www.sciencedirect.com/science/book/9780123971944
ISBN:	9780123971944 (electronic bk.)

Chi-squared goodness of fit tests with applications
Voinov, Vassiliy.

Chi-squared goodness of fit tests with applications[electronic resource] /V. Voinov, KIMEP University; Institute for Mathematics and Mathematical Modeling of the Ministry of Education and Science, Almaty, Kazakhstan, M. Nikulin, University Bordeaux-2, Bordeaux, France, N. Balakrishnan, McMaster University, Hamilton, Ontario, Canada. - Amsterdam :Elsevier/AP,2013. - xii, 229 p. :ill. ;24 cm.

Includes bibliographical references (p. 215-226) and index.

"If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the parameter is considered to be known). Until 1934, Pearson believed that the limiting distribution of the statistic in (1.1) will be the same if the unknown parameters of the null hypothesis are replaced by their estimates based on a sample; see, for example, Baird (1983), Plackett (1983, p. 63), Lindley (1996), Rao (2002), and Stigler (2008, p. 266). In this regard, it is important to reproduce the words of Plackett (1983, p. 69) concerning E. S. Pearson's opinion: "I knew long ago that KP (meaning Karl Pearson) used the 'correct' degrees of freedom for (a) difference between two samples and (b) multiple contingency tables. But he could not see that

ISBN: 9780123971944 (electronic bk.)

LCCN: 2012039862Subjects--Topical Terms:

182578
Chi-square test.

LC Class. No.: QA277.3 / .V65 2013

Dewey Class. No.: 519.5/6

Chi-squared goodness of fit tests with applications
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245 1 0 $a Chi-squared goodness of fit tests with applications $h [electronic resource] / $c V. Voinov, KIMEP University; Institute for Mathematics and Mathematical Modeling of the Ministry of Education and Science, Almaty, Kazakhstan, M. Nikulin, University Bordeaux-2, Bordeaux, France, N. Balakrishnan, McMaster University, Hamilton, Ontario, Canada.
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520 $a "If the number of sample observations n ! 1, the statistic in (1.1) will follow the chi-squared probability distribution with r-1 degrees of freedom. We know that this remarkable result is true only for a simple null hypothesis when a hypothetical distribution is specified uniquely (i.e., the parameter is considered to be known). Until 1934, Pearson believed that the limiting distribution of the statistic in (1.1) will be the same if the unknown parameters of the null hypothesis are replaced by their estimates based on a sample; see, for example, Baird (1983), Plackett (1983, p. 63), Lindley (1996), Rao (2002), and Stigler (2008, p. 266). In this regard, it is important to reproduce the words of Plackett (1983, p. 69) concerning E. S. Pearson's opinion: "I knew long ago that KP (meaning Karl Pearson) used the 'correct' degrees of freedom for (a) difference between two samples and (b) multiple contingency tables. But he could not see that $2 in curve fitting should be got asymptotically into the same category." Plackett explained that this crucial mistake of Pearson arose from to Karl Pearson's assumption "that individual normality implies joint normality." Stigler (2008) noted that this error of Pearson "has left a positive and lasting negative impression upon the statistical world." Fisher (1924) clearly showed 1 2 CHAPTER 1. A HISTORICAL ACCOUNT that the number of degrees of freedom of Pearson's test must be reduced by the number of parameters estimated from the sample"-- $c Provided by publisher.
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