Characterization of Power-Function Distribution through Expectation


For the characterization of the power function distribution, one needs any arbitrary non constant function only in place of independence of suitable function of order statistics, linear relation of conditional expectation, recurrence relations between expectations of function of order statistics, distributional properties of exponential distribution, record valves, lower record statistics, product of order statistics and Lorenz curve, etc. available in the literature. The goal of this research is not to give a different path-breaking approach for the characterization of power function distribution through the expectation of non constant function of random variable and provide a method to characterize the power function distribution as remark. Examples are given for the illustrative purpose.

Share and Cite:

M. Bhatt, "Characterization of Power-Function Distribution through Expectation," Open Journal of Statistics, Vol. 3 No. 6, 2013, pp. 441-443. doi: 10.4236/ojs.2013.36052.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] M. Fisz, “Characterization of Some Probability Distribution,” Skand. Aktuarietidskr, Vol. 41, No. 1-2, 1958, pp. 65-67.
[2] A. P. Basu, “On Characterizing the Exponential Distribution by Order Statistics,” Annals of the Institute of Statistical Mathematics, Vol. 17, No. 1, 1965, pp. 93-96.
[3] Z. Govindarajulu, “Characterization of Exponential and Power Distribution,” Skand. Aktuarietidskr, Vol. 41, 1966, pp. 132-136.
[4] A. C. Dallas, “Characterization Pareto and Power Distribution,” The Annals of Mathematical Statistics, Part A, Vol. 28, No. 1, 1976, pp. 491-497.
[5] M. L. Beg and S. N. U. A. Kirmani, “On a Characterization of Exponential and Related Distributions,” The Australian Journal of Statistics, Vol. 16, No. 3, 1974, pp. 163-166.
[6] H. N. Nagaraja, “On a Characterization Based on Record Valves,” The Australian Journal of Statistics, Vol. 19, No. 1, pp. 70-73.
[7] M. A. Ali and A. H. Khan, “Characterization of Some Types of Distributions,” Information and Management Sciences, Vol. 9, No. 2, 1998, pp. 1-9.
[8] M. Tavangar and M. Asadi, “Some New Characterization Results on Exponential and Related Distributions,” Bulletin of the Iranian Mathematical Society, Vol. 36, No. 1, 2010, pp. 257-272.
[9] M. Faizan and M. I. Khan, “A Characterization of Continuous Distributions through Lower Record Statistics,” Forum, Vol. 4, 2011, pp. 39-43.
[10] G. Arslan, “Characterization Based on Product of Order Statistics,” math.ST., 2011. arXiv 1110.2879v
[11] M. H. Alamatsaz, “An Integer-Valued PTH-Order Autoregressive Structure,” (INAR(p)) Process,” Journal of Applied Probability, Vol. 27, No. 2, 1990, pp. 314-324.
[12] S. Kotz and F.W. Steutel, “Note on a Characterization of Exponential Distributions,” Statistics & Probability Letters, Vol. 6, No. 3, 1988, pp. 201-203.
[13] A. A. Alzaid and M. A. Al-Osh, “An Integer-Valued PTH-Order Autoregressive Structure,” (INAR(p)) Process,” Journal of Applied Probability, Vol. 27, No. 2, 1990, pp. 314-324.
[14] T. S. K. Moothathu, “Characterization of Power Function Distribution through Property of Lorenz Curve,” Sankhy, Journal of Statistics, Series B, Vol. 48, Pt. 2, 1986, pp. 262-265.
[15] M. G. Kendall and A. Stuart, “The Advanced Theory of Statistics,” C. Griffin, London, 1958.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.