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Geometric dispersion models with real quadratic v-functions

Author

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  • Abid, Rahma
  • Kokonendji, Célestin C.
  • Masmoudi, Afif

Abstract

Geometric dispersion models, characterized by their v-functions, are recently introduced arising from geometric sums of exponential dispersion models and they exhibit many potential applications. In this paper, we classify all the real quadratic v-functions. Up to affinity, there are only six types of such models with unbounded domain: asymmetric Laplace, geometric and the four remaining ones are obtained by the exponential mixtures of Poisson, gamma, negative binomial and generalized hyperbolic secant distributions. Further, we find the seventh one which is geometric hybrid distribution, purely a quadratic v-function on bounded domain and, classically steep as well as unbounded ones but not geometric-steep.

Suggested Citation

  • Abid, Rahma & Kokonendji, Célestin C. & Masmoudi, Afif, 2019. "Geometric dispersion models with real quadratic v-functions," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 197-204.
    • Handle: RePEc:eee:stapro:v:145:y:2019:i:c:p:197-204
    DOI: 10.1016/j.spl.2018.09.010
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    References listed on IDEAS

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    1. Yacouba Boubacar Maïnassara & Célestin Kokonendji, 2014. "On normal stable Tweedie models and power-generalized variance functions of only one component," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 585-606, September.
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    Cited by:

    1. Célestin C. Kokonendji & Aboubacar Y. Touré & Rahma Abid, 2022. "On General Exponential Weight Functions and Variation Phenomenon," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 924-940, August.
    2. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2020. "Geometric Tweedie regression models for continuous and semicontinuous data with variation phenomenon," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 33-58, March.
    3. Rahma Abid & Célestin C. Kokonendji & Afif Masmoudi, 2021. "On Poisson-exponential-Tweedie models for ultra-overdispersed count data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(1), pages 1-23, March.
    4. Célestin C. Kokonendji & Aboubacar Y. Touré & Amadou Sawadogo, 2020. "Relative variation indexes for multivariate continuous distributions on $$[0,\infty )^k$$[0,∞)k and extensions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 285-307, June.

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