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Characterizations of probability distributions based on discrete p-monotonicity

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  • Sapatinas, Theofanis

Abstract

In this paper, a general characterization of a class of discrete self-decomposable distributions based on discrete p-monotonicity is obtained. This result can be thought as the discrete version of an earlier result due to Shanbhag (1972), Artikis (1982) and Alamatsaz (1985). Applying this result, discrete versions of some recent characterizations obtained by Kotz and Steutel (1988), Huang and Chen (1989) and Alamatsaz (1993) are given. Also, as a by-product of another related result, an extension of Forst's (1979) characterization of discrete self-decomposable Poisson mixtures is arrived at.

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  • Sapatinas, Theofanis, 1995. "Characterizations of probability distributions based on discrete p-monotonicity," Statistics & Probability Letters, Elsevier, vol. 24(4), pages 339-344, September.
    • Handle: RePEc:eee:stapro:v:24:y:1995:i:4:p:339-344
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    References listed on IDEAS

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    1. Kotz, S. & Steutel, F. W., 1988. "Note on a characterization of exponential distributions," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 201-203, February.
    2. Devroye, Luc, 1990. "A note on linnik's distribution," Statistics & Probability Letters, Elsevier, vol. 9(4), pages 305-306, April.
    3. Alamatsaz, M. H., 1993. "On characterizations of exponential and gamma distributions," Statistics & Probability Letters, Elsevier, vol. 17(4), pages 315-319, July.
    4. Devroye, Luc, 1993. "A triptych of discrete distributions related to the stable law," Statistics & Probability Letters, Elsevier, vol. 18(5), pages 349-351, December.
    5. Huang, Wen-Jang & Chen, Li-Sue, 1989. "Note on a characterization of gamma distributions," Statistics & Probability Letters, Elsevier, vol. 8(5), pages 485-487, October.
    6. van Harn, K. & Steutel, F.W., 1993. "Stability equations for processes with stationary independent increments using branching processes and Poisson mixtures," Stochastic Processes and their Applications, Elsevier, vol. 45(2), pages 209-230, April.
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    1. Sapatinas, Theofanis, 1999. "A characterization of the negative binomial distribution via [alpha]-monotonicity," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 49-53, October.

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