# Tail orderings and the total time on test transform

Applicationes Mathematicae (1996)

- Volume: 24, Issue: 1, page 77-86
- ISSN: 1233-7234

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topBartoszewicz, Jarosław. "Tail orderings and the total time on test transform." Applicationes Mathematicae 24.1 (1996): 77-86. <http://eudml.org/doc/219153>.

@article{Bartoszewicz1996,

abstract = {The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.},

author = {Bartoszewicz, Jarosław},

journal = {Applicationes Mathematicae},

keywords = {partial orderings; outliers; spacings; goodness-of-fit test; density-quantile function; total-time-on-test-transforms; stochastic tail orders},

language = {eng},

number = {1},

pages = {77-86},

title = {Tail orderings and the total time on test transform},

url = {http://eudml.org/doc/219153},

volume = {24},

year = {1996},

}

TY - JOUR

AU - Bartoszewicz, Jarosław

TI - Tail orderings and the total time on test transform

JO - Applicationes Mathematicae

PY - 1996

VL - 24

IS - 1

SP - 77

EP - 86

AB - The paper presents some connections between two tail orderings of distributions and the total time on test transform. The procedure for testing the pure-tail ordering is proposed.

LA - eng

KW - partial orderings; outliers; spacings; goodness-of-fit test; density-quantile function; total-time-on-test-transforms; stochastic tail orders

UR - http://eudml.org/doc/219153

ER -

## References

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- [2] R. E. Barlow, D. J. Bartholomew, J. M. Bremner and H. D. Brunk, Statistical Inference under Order Restrictions, Wiley, New York, 1972. Zbl0246.62038
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- [8] J. Bartoszewicz, Asymptotic distributions of tests for dispersive ordering, ibid. 15 (1992), 11-20. Zbl0774.62015
- [9] J. Bartoszewicz, Stochastic order relations and the total time on test transform, ibid. 22 (1995), 103-110. Zbl0811.62020
- [10] J. Bartoszewicz and T. Bednarski, On a test for dispersive ordering, ibid. 10 (1990), 355-362. Zbl0703.62058
- [11] K. A. Doksum, Starshaped transformations and the power of rank tests, Ann. Math. Statist. 40 (1969), 1167-1176. Zbl0188.50601
- [12] J. Hájek and Z. Šidák, Theory of Rank Tests, Academic Press, New York, 1967. Zbl0161.38102
- [13] M. J. Lawrance, Inequalities of s-ordered distributions, Ann. Statist. 3 (1975), 413-428. Zbl0305.62029
- [14] E. L. Lehmann, Comparing location experiments, ibid. 16 (1988), 521-533. Zbl0672.62008
- [15] W. Y. Loh, Bounds on ARE's for restricted classes of distributions defined via tail orderings, ibid. 12, 685-701. Zbl0598.62051
- [16] E. Parzen, Nonparametric statistical data modeling, J. Amer. Statist. Assoc. 74 (1979), 105-131. Zbl0407.62001
- [17] J. Rojo, A pure-tail ordering based on the ratio of the quantile functions, Ann. Statist. 20 (1992), 570-579. Zbl0745.62011
- [18] E. F. Schuster, Classification of probability laws by tail behavior, J. Amer. Statist. Assoc. 79 (1984), 936-939. Zbl0548.62019
- [19] E. Seneta, Regularly Varying Functions, Springer, New York, 1976. Zbl0324.26002
- [20] M. Shaked, Dispersive ordering of distributions, J. Appl. Probab. 9 (1982), 310-320. Zbl0481.60022
- [21] W. R. van Zwet, Convex Transformations of Random Variables, Math. Centrum, Amsterdam, 1964. Zbl0125.37102

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