Titlebook: Statistical Distributions in Scientific Work; Volume 5 — Inferenti Charles Taillie,Ganapati P. Patil,Bruno A. Baldess Book 1981 D. Reidel P

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https://doi.org/10.1007/978-94-009-8552-0Estimator; Fitting; Likelihood; best fit; calculus; function

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Chi-Square Goodness-of-Fit Tests Based on Dependent Observationsbservations which are obtained from a strictly stationary and strong-mixing random process. We conclude that the null distributions of the test statistics are largely determined by the multivariate probability structure of the process. A few examples are used to illustrate this point.

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An Asymptotically Distribution-Free Goodness-of-Fit Test for Families of Statistical Distributions Dgeneral conditions. The null distribution of the test statistic does not depend on the nuisance parameters and is asymptotically distribution-free. The paper gives a short table of its critical values and a table of its power against some alternatives.

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Conditionality Properties for the Bivariate Logarithmic Distribution with an Application to Goodnesses are derived (including, e.g., X|Y > X, X|Y - X = n), and are applied to the problem of grouping frequencies for a chi-square goodness-of-fit test for the homogeneous bivariate logarithmic distribution. The proposed procedure is objective and impartial with respect to rows and columns.

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A New Estimation Procedure for the Three-Parameter Lognormal Distributiones, has shown that the procedure is more efficient than maximum-likelihood, when samples are small. The procedure allows, also, hypothesis testing of lognormality. A table of percentage points is presented for this purpose. Finally, an example illustrates the application of the procedure.

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On the Asymptotic Distribution of the Multivariate Cramer-Von Mises and Hoeffding-Blum-Kiefer-Rosenbmultivariate Cramér-von Mises statistic. The second part is a preview of some developments in the asymptotic distribution theory of the Hoeffding-Blum-Kiefer-Rosenblatt independence criterion in that the there quoted 1980 joint results with Derek S. Cotterill of the Department of national Defence, Ottawa, have not yet appeared elsewhere.

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On Tests of Independence under Bivariate Exponential Modelsussion then turns to the bivariate exponential distribution (BVE) of Marshall and Olkin (1967) and the absolutely continuous bivariate exponential distribution (ACBVE) of Block and Basu (1974). Power calculations are carried out for several statistics, and asymptotic relative efficiencies are calculated.

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On Tests for Detecting Change in the Multivariate Meanhe alternative that a change has occurred at some unknown point r, (i.e., .. = .2 =… = .. ≠ .. =…= ..). The ..’s are assumed to be normally distributed with common unknown covariance. An estimate of the change point r is also given.

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A Two-Dimensional T-Distribution and a New Test with Flexible Type I Error Controlthe possibility that one of the component hypotheses may be principal, i.e., scientifically more relevant or important than the other. In this we use some properties of a bivariate t-distribution to construct a test which permits asymmetric treatment of the two component hypotheses. The proposed test is shown to be unbiased and consistent.

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