Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

A CHARACTERIZATION OF THE POWER FUNCTION DISTRIBUTION BY INDEPENDENT PROPERTY OF LOWER RECORD VALUES

  • Received : 2012.09.24
  • Accepted : 2013.01.11
  • Published : 2013.05.15
Download PDF
⟨ Previous Next ⟩

Abstract

We prove a characterization of the power function distribution by lower record values. We prove that $F(x)=(\frac{x}{a})^{\alpha}$ for all $x$, 0 < $x$ < $a$, ${\alpha}$ > 0 and $a$ > 0 if and only if $\frac{X_{L(n)}}{X_{L(m)}}$ and $X_{L(m)}$ are independent for $1{\leq}m$ < $n$.

Keywords

References

  1. J. Aczel, Lectures on Functional Equation and Their Applications, Academic Press, Newyork, 1966.
  2. M. Ahsanullah, Record Statistics, Nova science Publishers, Inc. NJ, USA, 1995.
  3. M. Ahsanullah and Z. Raqab, Bounds and Characterizations of Record Statistics, Nova science Publishers, Inc, 2006.
  4. M. Y. Lee and E. H. Lim, On Characterizations of the Weibull distribution by the independent property of record values, J. Chungcheong Math. Soc. 23 (2010), no. 2, 245-250.

Cited by

  1. The modified Power function distribution vol.4, pp.1, 2017, https://doi.org/10.1080/23311835.2017.1319592
  2. Characterization and Goodness-of-Fit Test of Pareto and Some Related Distributions Based on Near-Order Statistics vol.2020, pp.None, 2013, https://doi.org/10.1155/2020/4262574