충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제22권2호
  • /
  • Pages.149-153
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  • 2009
  • /
  • 1226-3524(pISSN)
  • /
  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
권호 표지

CHARACTERIZATIONS OF THE LOMAX, EXPONENTIAL AND PARETO DISTRIBUTIONS BY CONDITIONAL EXPECTATIONS OF RECORD VALUES

  • 투고 : 2009.01.07
  • 심사 : 2009.02.17
  • 발행 : 2009.06.30
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초록

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.

키워드

참고문헌

  1. M. Ahsanuallah, Record Statistics, Nova Science publishers, Inc, Commack NY, 1995.
  2. M. Y. Lee, S. K. Chang and K. H. Jung, Characterizations of the exponential distribution by order statistics and conditional expectations of record values, Commun. Korea Math. Soc. 17 (2002), 535-540. https://doi.org/10.4134/CKMS.2002.17.3.535
  3. H. N. Nagaraja, On a characterization based on record values, Austial. J. Statist 20 (1977), 70-73.