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

Franciszek Czekała

Applicationes Mathematicae (1996)

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

Abstract

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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].

How to cite

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Czekała, 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

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  1. N. Cressie (1976), On the logarithms of high-order spacings, Biometrika 63, 343-355. Zbl0331.62036
  2. F. Czekała (1993), Asymptotic distributions of statistics based on logarithms of spacings, Zastos. Mat. 21, 511-519. Zbl0805.62019
  3. 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
  4. J. R. Gebert and B. K. Kale (1969), Goodness of fit tests based on discriminatory information, Statist. Hefte 3, 192-200. Zbl0179.24102
  5. 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. 
  6. 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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