Characterizations of power distributions via moments of order statistics and record values

Z. Grudzień; D. Szynal

Applicationes Mathematicae (1999)

  • Volume: 26, Issue: 4, page 467-475
  • ISSN: 1233-7234

Abstract

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Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.

How to cite

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Grudzień, Z., and Szynal, D.. "Characterizations of power distributions via moments of order statistics and record values." Applicationes Mathematicae 26.4 (1999): 467-475. <http://eudml.org/doc/219252>.

@article{Grudzień1999,
abstract = {Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.},
author = {Grudzień, Z., Szynal, D.},
journal = {Applicationes Mathematicae},
keywords = {power; sample; uniform distributions; record values; samples; uniform distribution},
language = {eng},
number = {4},
pages = {467-475},
title = {Characterizations of power distributions via moments of order statistics and record values},
url = {http://eudml.org/doc/219252},
volume = {26},
year = {1999},
}

TY - JOUR
AU - Grudzień, Z.
AU - Szynal, D.
TI - Characterizations of power distributions via moments of order statistics and record values
JO - Applicationes Mathematicae
PY - 1999
VL - 26
IS - 4
SP - 467
EP - 475
AB - Power distributions can be characterized by equalities involving three moments of order statistics. Similar equalities involving three moments of k-record values can also be used for such a characterization. The case of samples with random sizes is also considered.
LA - eng
KW - power; sample; uniform distributions; record values; samples; uniform distribution
UR - http://eudml.org/doc/219252
ER -

References

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  1. [1] M. Ahsanullah, Characteristic properties of order statistics based on random sample size from an exponential distribution, Statist. Neerlandica 42 (1988), 193-197. Zbl0715.62021
  2. [2] H. A. David, Order Statistics in Probability and Mathematical Statistics, Wiley, 1970. 
  3. [3] W. Dziubdziela and B. Kopociński, Limiting properties of the kth record values, Zastos. Mat. 15 (1976), 187-190. Zbl0337.60023
  4. [4] Z. Grudzień and D. Szynal, Characterizations of distributions by moments of order statistics when the sample size is random, Appl. Math. (Warsaw) 23 (1995), 305-318. Zbl0836.62014
  5. [5] Z. Grudzień and D. Szynal, Characterization of continuous distributions in terms of moments of extremal statistics, J. Math. Sci. 81 (1996), 2912-2936. Zbl0871.62016
  6. [6] Z. Grudzień and D. Szynal, Characterizations of uniform and exponential distributions via moments of the kth record values randomly indexed, Appl. Math. (Warsaw) 24 (1997), 307-314. 
  7. [7] G. D. Lin, Characterizations of distribution via moments of order statistics: A survey and comparison of methods, in: Statistical Data Analysis and Inference, Y. Dodge (ed.), North-Holland, 1989, 297-307. Zbl0735.62013
  8. [8] Y. H. Too and G. D. Lin, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359. Zbl0666.62010
  9. [9] G. D. Lin and Y. H. Too, Characterization of distributions via moments of order statistics when sample size is random, Southeast Asian Bull. Math. 15 (1991), 139-144. Zbl0742.62010

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