Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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CHARACTERIZATION OF STANDARD EXTREME VALUE DISTRIBUTIONS USING RECORDS

  • Skrivankova, Valeria (Institute of Mathematics P. J. Safarik University of Kosice) ;
  • Juhas, Matej (Institute of Mathematics P. J. Safarik University of Kosice)
  • Received : 2010.07.09
  • Accepted : 2011.08.25
  • Published : 2011.09.30
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Abstract

The paper deals with characterization of standard Gumbel distribution and standard $Fr{\acute{e}}chet$ distribution and was motivated by [4], where the Weibull distribution is characterized. We present criterions using the independence of some suitable functions of lower records in a sequence of independent identically distributed random variables $\{X_n,\;n{\geq}1\}$.

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References

  1. J. ACZEL, Lectures on Functional Equations and Their Applications, Academic Press, NY, 1966.
  2. M. AHSANULLAH, Record values - theory and application, University Press of America, Inc., Lanham, Maryland, USA, 2005, ISBN 0-7618-2794-3.
  3. S. K. CHANG, Characterizations of the Pareto distribution by the independence of record values, J. Chungcheong Math. Soc. 20 (2007), no. 1 , 51-57.
  4. M. Y. LEE and E. H. LIM, On characterizations of the Weibull distribution by the independent property of record value, J. Chungcheong Math. Soc. 23 (2010), no. 2 , 245-250.
  5. V. SKRIVANKOVA and M. JUHAS, Records in Non-life Insurance, IM Preprint, series A, No. 9/2010, June 2010.