Download PDF - Characterizations of power distributions via moments of order statistics and record valuesAll rights reserved. Copyright exceptions and limitations apply

ArticleOriginal scientific text

Title

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

Authors 1, 1

Affiliations

  1. Department of Mathematics, Maria Curie-Skłodowska University, Pl. M. Curie-Skłodowskiej 1, 20-031 Lublin, Poland

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.

Keywords

ENG
power, sample, uniform distributions, record values

Bibliography

  1. M. Ahsanullah, Characteristic properties of order statistics based on random sample size from an exponential distribution, Statist. Neerlandica 42 (1988), 193-197.
  2. H. A. David, Order Statistics in Probability and Mathematical Statistics, Wiley, 1970.
  3. W. Dziubdziela and B. Kopociński, Limiting properties of the kth record values, Zastos. Mat. 15 (1976), 187-190.
  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.
  5. Z. Grudzień and D. Szynal, Characterization of continuous distributions in terms of moments of extremal statistics, J. Math. Sci. 81 (1996), 2912-2936.
  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. 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.
  8. Y. H. Too and G. D. Lin, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359.
  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.
Applicationes Mathematicae
1999/26/4
Export to PBN, Opens in new tab
Pages:
467-475
Main language of publication
English
Received
1999-05-07
Accepted
1999-07-12
Published
1999
Exact and natural sciences