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

Applicationes Mathematicae (1996)

- Volume: 23, Issue: 4, page 405-416
- ISSN: 1233-7234

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topCzekała, Franciszek. "Normalizing constants for a statistic based on logarithms of disjoint m-spacings." Applicationes Mathematicae 23.4 (1996): 405-416. <http://eudml.org/doc/219142>.

@article{Czekała1996,

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].},

author = {Czekała, Franciszek},

journal = {Applicationes Mathematicae},

keywords = {asymptotic normality; higher-order spacings; step density function; logarithms of disjoint -spacings; mean; variance; uniform distribution},

language = {eng},

number = {4},

pages = {405-416},

title = {Normalizing constants for a statistic based on logarithms of disjoint m-spacings},

url = {http://eudml.org/doc/219142},

volume = {23},

year = {1996},

}

TY - JOUR

AU - Czekała, Franciszek

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

JO - Applicationes Mathematicae

PY - 1996

VL - 23

IS - 4

SP - 405

EP - 416

AB - 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].

LA - eng

KW - asymptotic normality; higher-order spacings; step density function; logarithms of disjoint -spacings; mean; variance; uniform distribution

UR - http://eudml.org/doc/219142

ER -

## References

top- N. Cressie (1976), On the logarithms of high-order spacings, Biometrika 63, 343-355. Zbl0331.62036
- F. Czekała (1993), Asymptotic distributions of statistics based on logarithms of spacings, Zastos. Mat. 21, 511-519. Zbl0805.62019
- G. E. Del Pino (1979) On the asymptotic distribution of k-spacings with applications to goodness of fit tests, Ann. Statist. 7, 1058-1065. Zbl0425.62026
- J. R. Gebert and B. K. Kale (1969), Goodness of fit tests based on discriminatory information, Statist. Hefte 3, 192-200. Zbl0179.24102
- S. R. Jammalamadaka and R. C. Tiwari (1986), Efficiencies of some disjoint spacings tests relative to a ${\chi}^{2}$ 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. Zbl0176.48604

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