# On two tests based on disjoint m-spacings

Applicationes Mathematicae (1998)

- Volume: 25, Issue: 3, page 359-373
- ISSN: 1233-7234

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topCzekała, Franciszek. "On two tests based on disjoint m-spacings." Applicationes Mathematicae 25.3 (1998): 359-373. <http://eudml.org/doc/219209>.

@article{Czekała1998,

abstract = {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.},

author = {Czekała, Franciszek},

journal = {Applicationes Mathematicae},

keywords = {step densities; disjoint m-spacings; limit distributions; Bahadur approximate efficiency},

language = {eng},

number = {3},

pages = {359-373},

title = {On two tests based on disjoint m-spacings},

url = {http://eudml.org/doc/219209},

volume = {25},

year = {1998},

}

TY - JOUR

AU - Czekała, Franciszek

TI - On two tests based on disjoint m-spacings

JO - Applicationes Mathematicae

PY - 1998

VL - 25

IS - 3

SP - 359

EP - 373

AB - 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.

LA - eng

KW - step densities; disjoint m-spacings; limit distributions; Bahadur approximate efficiency

UR - http://eudml.org/doc/219209

ER -

## References

top- R. R. Bahadur (1960), Stochastic comparison of tests, Ann. Math. Statist. 31, 276-295. Zbl0201.52203
- J. Bartoszewicz (1995), Bahadur and Hodges-Lehmann approximate efficiencies of tests based on spacings, Statist. Probab. Lett. 23, 211-220. Zbl0820.62039
- N. Cressie (1976), On the logarithms of high-order spacings, Biometrika 63, 343-355. Zbl0331.62036
- F. Czekała (1996), Normalizing constants for a statistic based on logarithms of disjoint spacings, Appl. Math. (Warsaw) 23 (4), 405-416. Zbl0843.62018
- D. A. Darling (1953), On a class of problems relating to the random division of an interval, Ann. Math. Statist. 24, 239-253. Zbl0053.09902
- 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
- F. Proschan and R. Pyke (1964), Asymptotic normality of certain test statistics of exponentiality, Biometrika 51, 253-255. Zbl0192.25803

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