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On characterizations and variance bounds of discrete α-unimodality

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Abstract

Characterizations of α-unimodality for integer-valued random variables about a specific mode are established in terms of their probability mass functions, distribution functions and characteristic functions. Using these characterizations variance lower bounds in terms of α and the mode are derived. For α=1 all these results are reduced to ordinary unimodality. The new variance lower bounds for discrete unimodality is sharper than its continuous counterpart. An upper bound for the variance of discrete unimodal distribution defined on a finite support is discussed.

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Authors and Affiliations

  1. Department of Statistics and Operations Research, College of Science, King Saud University, P. O. Box 2455, 11451, Riyadh, Saudi Arabia

    A. M. Abouammoh & A. F. Mashhour

  2. Department of Mathematics, College of Science, Almansoura University, Almansoura, Egypt

    A. M. Ali

Authors
  1. A. M. Abouammoh
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  2. A. M. Ali
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  3. A. F. Mashhour
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Abouammoh, A.M., Ali, A.M. & Mashhour, A.F. On characterizations and variance bounds of discrete α-unimodality. Statistical Papers 35, 151–161 (1994). https://doi.org/10.1007/BF02926408

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  • DOI: https://doi.org/10.1007/BF02926408

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