CHARACTERIZATIONS OF THE WEIBULL DISTRIBUTION BY THE INDEPENDENCE OF THE UPPER RECORD VALUES
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This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that X 2 WEI(); if and only if XU(n+1) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent or XU(n) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent. And also we establish that X 2 WEI(); if and only if XU(n+1) ¡ XU(n) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent.
Abstract
This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that X 2 WEI(); if and only if XU(n+1) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent or XU(n) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent. And also we establish that X 2 WEI(); if and only if XU(n+1) ¡ XU(n) XU(n+1) + XU(n) and XU(n+1) for n ¸ 1 are independent.
참고문헌 (4)
- J. Aczel, "Lectures on Functional Equations and Their Applications" (1966), Academic Press
- M. Ahsanuallah, "Record Statistics" (1995), Nova Science Publishers, Inc
- J. Galambos, "Characterization of Probability Distributions. Lecture Notes in Mathematics" (1978), Springer-Verlag
- M.Y. Lee, "Characterizations based on the independence of the exponential and Pareto distributions by record values", J. Appl. Math. & Computing, 18(1-2), pp.497~503 (2005)