Characterizations of distributions by moments of order statistics when the sample size is random

Zofia Grudzień; Dominik Szynal

Applicationes Mathematicae (1995)

  • Volume: 23, Issue: 3, page 305-318
  • ISSN: 1233-7234

Abstract

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We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.

How to cite

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Grudzień, Zofia, and Szynal, Dominik. "Characterizations of distributions by moments of order statistics when the sample size is random." Applicationes Mathematicae 23.3 (1995): 305-318. <http://eudml.org/doc/219133>.

@article{Grudzień1995,
abstract = {We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.},
author = {Grudzień, Zofia, Szynal, Dominik},
journal = {Applicationes Mathematicae},
keywords = {Poisson distribution; logarithmic series; binomial; random sample size; geometrical; order statistics; recurrence formula; uniform distribution; negative binomial; moments; characterizations; moments of order statistics},
language = {eng},
number = {3},
pages = {305-318},
title = {Characterizations of distributions by moments of order statistics when the sample size is random},
url = {http://eudml.org/doc/219133},
volume = {23},
year = {1995},
}

TY - JOUR
AU - Grudzień, Zofia
AU - Szynal, Dominik
TI - Characterizations of distributions by moments of order statistics when the sample size is random
JO - Applicationes Mathematicae
PY - 1995
VL - 23
IS - 3
SP - 305
EP - 318
AB - We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
LA - eng
KW - Poisson distribution; logarithmic series; binomial; random sample size; geometrical; order statistics; recurrence formula; uniform distribution; negative binomial; moments; characterizations; moments of order statistics
UR - http://eudml.org/doc/219133
ER -

References

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  1. [1] T. A. Azlarov and N. A. Volodin, Characterizations Problems Associated with the Exponential Distribution, Springer, New York, 1986. Zbl0624.62020
  2. [2] H. A. David, Order Statistics, Wiley Ser. Probab. Math. Statist., Wiley, New York, 1970. 
  3. [3] J. Galambos and S. Kotz, Characterizations of Probability Distributions. A Unified Approach with an Emphasis on Exponential and Related Models, Lecture Notes in Math. 8, Springer, Berlin, 1978. Zbl0381.62011
  4. [4] N. L. Johnson, S. Kotz and A. W. Kemp, Univariate Discrete Distributions, 2nd ed., Wiley, New York, 1992. 
  5. [5] G. D. Lin, Characterizations of distributions via moment of order statistics. A survey and comparison of methods, in: Statistical Data Analysis and Inference, Y. Dodge (ed.), North-Holland, Amsterdam, 1989, 297-307. Zbl0735.62013
  6. [6] G. D. Lin and Y. H. Too, Characterizations of uniform and exponential distributions, Statist. Probab. Lett. 7 (1989), 357-359. Zbl0666.62010
  7. [7] G. D. Lin and Y. H. Too, Characterizations of distributions via moments of order statistics when sample size is random, Southeast Asian Bull. Math. 15 (1991), 139-144. Zbl0742.62010
  8. [8] N. De Pril, Moments of a class of compound distributions, Scand. Actuar. J. 1986, 117-120. Zbl0648.62017

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