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A characterization of the exponential distribution by higher order gap

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SupposeX is a non-negative random variable with an absolutely continuous (with respect to Lebesgue measure) distribution functionF (x) and the corresponding probability density functionf(x). LetX 1,X 2,...,X n be a random sample of sizen fromF andX i,n is thei-th smallest order statistics. We define thej-th order gapg i,j(n) asg i,j(n)=X i+j,n−Xi,n′ 1≤i<n, 1≤n≦n−i. In this paper a characterization of the exponential distribution is given by considering a distribution property ofg i,j(n).

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References

  • Ahsanuallah, M.: A characterization of the exponential distribution. A Modern Course on Statistical Distribution in Scientific Work. Ed. by G.P. Patil, S. Kotz, and J.K. Ord. Dordrecht 1975, 131–135.

  • Galambos, J., andS. Kotz: Characterizations of Probability Distributions. New York 1978.

  • Rossberg, H.J.: Characterizations of the exponential and the Pareto distributions by means of some properties of the distributions which the differences and quotients of order statistics are subject to. Math. Operationsforschung und Statistik3, 1972, 207–216.

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  1. Department of Statistics, Temple University, 19122, Phildalphia, PA, USA

    M. Ahsanullah

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  1. M. Ahsanullah
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Ahsanullah, M. A characterization of the exponential distribution by higher order gap. Metrika 31, 323–326 (1984). https://doi.org/10.1007/BF01915219

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  • DOI: https://doi.org/10.1007/BF01915219

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