Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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On Bounds for Moments of Unimodal Distributions

  • Sharma, R. (Department of Mathematics & Statistics, Himachal Pradesh University) ;
  • Bhandaria, R. (Department of Mathematics & Statistics, Himachal Pradesh University)
  • Received : 2013.10.08
  • Accepted : 2014.04.21
  • Published : 2014.05.31
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Abstract

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

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References

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