Normalizing constants for a statistic based on logarithms of disjoint m-spacings

• Autorzy: Franciszek Czekała
• Języki publikacji: EN

Abstrakty

EN

The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance 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].

Słowa kluczowe

EN

asymptotic normality; higher-order spacings; step density function

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 1995-1996
• Tom: 23
• Numer: 4
• Strony: 405-416

Daty

wydano

1996

otrzymano

1995-01-24

Twórcy

autor

Franciszek Czekała

• Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Bibliografia

• N. Cressie (1976), On the logarithms of high-order spacings, Biometrika 63, 343-355.
• F. Czekała (1993), Asymptotic distributions of statistics based on logarithms of spacings, Zastos. Mat. 21, 511-519.
• 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.