ArticleOriginal scientific text
Title
Normalizing constants for a statistic based on logarithms of disjoint m-spacings
Authors 1
Affiliations
- Mathematical Institute, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Abstract
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].
Keywords
asymptotic normality, higher-order spacings, step density function
Bibliography
- 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
- B. K. Kale (1969), Unified derivation of tests of goodness of fit based on spacings, Sankhyā Ser. A 31, 43-48.
Pages:
405-416
Main language of publication
English
Received
1995-01-24
Published
1996
Exact and natural sciences