Tail orderings and the total time on test transform

Jarosław Bartoszewicz

Applicationes Mathematicae (1996)

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

Abstract

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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.

How to cite

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Bartoszewicz, 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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  1. [1] A. A. Alzaid and M. Al-Osh, Ordering probability distributions by tail behavior, Statist. Probab. Lett. 8 (1989), 185-188. 
  2. [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
  3. [3] R. E. Barlow and K. A. Doksum, Isotonic tests for convex orderings, in: Proc. 6th Berkeley Sympos. Math. Statist. Probab. I, Univ. of Calif. Press, 1972, 293-323. Zbl0231.62061
  4. [4] R. E. Barlow and F. Proschan, The Statistical Theory of Reliability, Holt, Rinehart and Winston, New York, 1975. Zbl0379.62080
  5. [5] R. E. Barlow and W. R. van Zwet, Asymptotic properties of isotonic estimators for the generalized failure rate function, in: Nonparametic Techniques in Statistical Inference, Cambridge Univ. Press, Cambridge, 1970, 159-176. 
  6. [6] V. Barnett and T. Lewis, Outliers in Statistical Data, Wiley, New York, 1978. Zbl0377.62001
  7. [7] J. Bartoszewicz, Dispersive ordering and the total time on test transformation, Statist. Probab. Lett. 4 (1986), 285-288. Zbl0622.62052
  8. [8] J. Bartoszewicz, Asymptotic distributions of tests for dispersive ordering, ibid. 15 (1992), 11-20. Zbl0774.62015
  9. [9] J. Bartoszewicz, Stochastic order relations and the total time on test transform, ibid. 22 (1995), 103-110. Zbl0811.62020
  10. [10] J. Bartoszewicz and T. Bednarski, On a test for dispersive ordering, ibid. 10 (1990), 355-362. Zbl0703.62058
  11. [11] K. A. Doksum, Starshaped transformations and the power of rank tests, Ann. Math. Statist. 40 (1969), 1167-1176. Zbl0188.50601
  12. [12] J. Hájek and Z. Šidák, Theory of Rank Tests, Academic Press, New York, 1967. Zbl0161.38102
  13. [13] M. J. Lawrance, Inequalities of s-ordered distributions, Ann. Statist. 3 (1975), 413-428. Zbl0305.62029
  14. [14] E. L. Lehmann, Comparing location experiments, ibid. 16 (1988), 521-533. Zbl0672.62008
  15. [15] W. Y. Loh, Bounds on ARE's for restricted classes of distributions defined via tail orderings, ibid. 12, 685-701. Zbl0598.62051
  16. [16] E. Parzen, Nonparametric statistical data modeling, J. Amer. Statist. Assoc. 74 (1979), 105-131. Zbl0407.62001
  17. [17] J. Rojo, A pure-tail ordering based on the ratio of the quantile functions, Ann. Statist. 20 (1992), 570-579. Zbl0745.62011
  18. [18] E. F. Schuster, Classification of probability laws by tail behavior, J. Amer. Statist. Assoc. 79 (1984), 936-939. Zbl0548.62019
  19. [19] E. Seneta, Regularly Varying Functions, Springer, New York, 1976. Zbl0324.26002
  20. [20] M. Shaked, Dispersive ordering of distributions, J. Appl. Probab. 9 (1982), 310-320. Zbl0481.60022
  21. [21] W. R. van Zwet, Convex Transformations of Random Variables, Math. Centrum, Amsterdam, 1964. Zbl0125.37102

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