Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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Asymptotic Properties of Upper Spacings

  • Yun, Seok-Hoon (Department of Applied Statistics, University of Suwon, Kyonggi-do, 445-743)
  • Published : 1997.09.01
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Abstract

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

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References

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