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Smooth Tests of Goodness of Fit
Technometrics, 1991AbstractSmooth tests of goodness of fit assess the fit of data to a given probability density function within a class of alternatives that differs ‘smoothly’ from the null model. These alternatives are characterized by their order: the greater the order the richer the class of alternatives. The order may be a specified constant, but data‐driven methods
Rayner, J. C. W., Thas, O., Best, D. J.
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Length tests for goodnesss-of-fit
Biometrika, 1991Consider an i.i.d. sample X 1,..., X n with distribution function F, which throughout is assumed to be twice continuously differentiable with support [0,1] and strictly positive derivative on [0,1]. Denote by $$0={X_{0:n}}\leqslant {X_{1:n}}\leqslant\cdots\leqslant{X_{n:n}}\leqslant{X_{n+1:n}}=1$$ (1) the order statistics, and the spacings by
Reschenhofer, Erhard, Bomze, Immanuel
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A new goodness-of-fit statistical test
Intelligent Decision Technologies, 2007We introduce a new concept of nonparametric test for statistically deciding if a model fits a sample of data well. The employed statistic is the empirical cumulative distribution (e.c.d.f.) of the measure of the blocks determined by the ordered sample.
B. Apolloni, S. Bassis
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Order Statistics in Goodness-of-Fit Testing
IEEE Transactions on Reliability, 2001Our new method uses order statistics to judge the fit of a distribution to data. A test-statistic based on quantiles of order-statistics compares favorably with the Kolmogorov-Smirnov (K-S) and Anderson-Darling (A-D) test statistics. The performance of this new goodness-of-fit test statistic is examined with simulation experiments.
Andrew G. Glen +2 more
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Goodness-of-Fit Tests on a Circle. II
Biometrika, 1961Abstract : A statistical analysis is made by use of the null hypothesis test for random samples which have been drawn from a population with the continuous distribution function F(x). It is useful for distributions on a circle since its value does not depend on the arbitrary point chosen to begin cumulating the probability density and the sample points.
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Statistische Hefte, 1967
The authors propose a new test of goodness of fit for the simple null hypothesis that the actual distribution is equal to a given, everywhere continuous distribution function. Under theNeyman-Pearson setup they obtain a test which (a) is meaningful without reference to any specific set of alternatives, and (b) is based on the fact we tend to dis ...
Kale, B. K., Godambe, V. P.
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The authors propose a new test of goodness of fit for the simple null hypothesis that the actual distribution is equal to a given, everywhere continuous distribution function. Under theNeyman-Pearson setup they obtain a test which (a) is meaningful without reference to any specific set of alternatives, and (b) is based on the fact we tend to dis ...
Kale, B. K., Godambe, V. P.
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Statistica Neerlandica, 1966
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Vandewiele, Georges, De Witte, Paul
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Vandewiele, Georges, De Witte, Paul
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»Smooth test» for goodness of fit
Scandinavian Actuarial Journal, 1937Abstract Dedicated to the memory of Karl Pearson (27 March 1857—27 April 1936) who originated the problem of a test for goodness of fit and was first to advance its solution.
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Randomized goodness of fit tests
Kybernetika, 2011Summary: Classical goodness-of-fit tests are no longer asymptotically distributional free if parameters are estimated. For a parametric model and the maximum likelihood estimator the empirical processes with estimated parameters is asymptotically transformed into a time transformed Brownian bridge by adding an independent Gaussian process that is ...
Friedrich Liese, Bing Liu
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1998
Goodness-of-fit tests are used to validate the use of a particular distribution to describe data arising from sampling or experimentation. Numerous goodness-of-fit tests have been developed. The power divergence family of test statistics includes Pearson’s chi-squared test, the likelihood ratio test, and the Freeman-Tukey chi-squared test.
Linda J. Young, Jerry H. Young
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Goodness-of-fit tests are used to validate the use of a particular distribution to describe data arising from sampling or experimentation. Numerous goodness-of-fit tests have been developed. The power divergence family of test statistics includes Pearson’s chi-squared test, the likelihood ratio test, and the Freeman-Tukey chi-squared test.
Linda J. Young, Jerry H. Young
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