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On characterizations of exponential and gamma distributions

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  • Alamatsaz, M. H.

Abstract

As an interpretation of a general characterization concerning [alpha]-unimodal distributions due to Alamatsaz, the solution of the equation of recent interest is found where M and K (M > K) are integers, [alpha] > 0, U is uniformly distributed on (0, 1), Zi's are identical, Z1,...,ZK are independent and U, ZK+1,...,ZK+M are also independent. This yields several characterizations of exponential and gamma distributions and contains previous results of Kotz and Steutel (1988), Huang and Chen (1989), Yeo and Milne (1991) and Devroye (1990) in this connection. Then, a multivariate extension is discussed.

Suggested Citation

  • Alamatsaz, M. H., 1993. "On characterizations of exponential and gamma distributions," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 315-319, July.
    • Handle: RePEc:eee:stapro:v:17:y:1993:i:4:p:315-319
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    Citations

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    Cited by:

    1. Mahdi Alimohammadi & Mohammad Hossein Alamatsaz & Erhard Cramer, 2016. "Convolutions and generalization of logconcavity: Implications and applications," Naval Research Logistics (NRL), John Wiley & Sons, vol. 63(2), pages 109-123, March.
    2. Sapatinas, Theofanis, 1995. "Characterizations of probability distributions based on discrete p-monotonicity," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 339-344, September.
    3. Anthony Pakes, 1994. "Necessary conditions for characterization of laws via mixed sums," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 797-802, December.
    4. Hazhir Homei & Saralees Nadarajah, 2018. "On Products and Mixed Sums of Gamma and Beta Random Variables Motivated by Availability," Methodology and Computing in Applied Probability, Springer, vol. 20(2), pages 799-810, June.

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