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Applicationes Mathematicae

1998-1999 | 25 | 3 | 359-373
Tytuł artykułu

On two tests based on disjoint m-spacings

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
This paper is concerned with the properties of two statistics based on the logarithms of disjoint m-spacings. The asymptotic normality is established in an elementary way and exact and asymptotic means and variances are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1]. Bahadur approximate efficiency of tests based on those statistics is found for such alternatives.
Słowa kluczowe
EN
Czasopismo
Rocznik
Tom
Numer
Strony
359-373
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-09-25
Twórcy
autor
• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
• R. R. Bahadur (1960), Stochastic comparison of tests, Ann. Math. Statist. 31, 276-295.
• J. Bartoszewicz (1995), Bahadur and Hodges-Lehmann approximate efficiencies of tests based on spacings, Statist. Probab. Lett. 23, 211-220.
• N. Cressie (1976), On the logarithms of high-order spacings, Biometrika 63, 343-355.
• F. Czekała (1996), Normalizing constants for a statistic based on logarithms of disjoint spacings, Appl. Math. (Warsaw) 23 (4), 405-416.
• D. A. Darling (1953), On a class of problems relating to the random division of an interval, Ann. Math. Statist. 24, 239-253.
• G. E. Del Pino (1979), On the asymptotic distribution of k-spacings with applications to goodness of fit tests, Ann. Statist. 7, 1058-1065.
• J. R. Gebert and B. K. Kale (1969), Goodness of fit tests based on discriminatory information, Statist. Hefte 3, 192-200.
• S. R. Jammalamadaka and R. C. Tiwari (1986), Efficiencies of some disjoint spacings tests relative to a $χ^2$ test, in: M. L. Puri, J. Vilaplana and W. Wertz (eds.), New Perspectives in Theoretical and Applied Statistics, Wiley, New York, 311-318.
• B. K. Kale (1969), Unified derivation of tests of goodness of fit based on spacings, Sankhyā Ser. A 31, 43-48.
• F. Proschan and R. Pyke (1964), Asymptotic normality of certain test statistics of exponentiality, Biometrika 51, 253-255.
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