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Variance upper bounds and convolutions of [alpha]-unimodal distributions

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  • Abouammoh, A. M.
  • Mashhour, A. F.

Abstract

The concept of [alpha]-uniform for generating an [alpha]-unimodal discrete distribution is introduced. Upper bounds for the variance of discrete [alpha]-unimodal distributions are established. Sufficient conditions for the convolution of [alpha]-unimodal distributions about a to be [alpha]-unimodal about the same mode are derived. These results are reduced to the usual discrete uniform and discrete unimodal distributions for [alpha] = 1. The paper includes other related results.

Suggested Citation

  • Abouammoh, A. M. & Mashhour, A. F., 1994. "Variance upper bounds and convolutions of [alpha]-unimodal distributions," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 281-289, November.
    • Handle: RePEc:eee:stapro:v:21:y:1994:i:4:p:281-289
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    Cited by:

    1. Martín Egozcue & Luis Fuentes García, 2017. "The variance upper bound for a mixed random variable," Documentos de Trabajo/Working Papers 1707, Facultad de Ciencias Empresariales y Economia. Universidad de Montevideo..
    2. Mashhour, A. F., 1996. "Some results on discrete [alpha]-unimodality," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 31-36, March.

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