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On normal stable Tweedie models and power-generalized variance functions of only one component

Author

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  • Yacouba Boubacar Maïnassara
  • Célestin Kokonendji

Abstract

As an extension to normal gamma and normal inverse Gaussian models, all normal stable Tweedie (NST) models are introduced for getting a simple form of the determinant of the covariance matrix, so-called generalized variance. As alternatives to the standard normal model, multivariate NST models are composed by a fixed univariate stable Tweedie variable having a positive value domain, and the remaining random variables given the fixed one are real independent Gaussian variables with the same variance equal to the fixed component. Within the framework of exponential dispersion models, a new form of variance functions is firstly established. Then, their generalized variance functions are shown to be powers of only the fixed mean component. Their modified Lévy measures are generally of the normal gamma type, which is connected to NST models through some Monge–Ampère equations. Two kinds of generalized variance estimators are discussed and variance modelling under only observations of normal terms is evoked. Finally, reasonable extensions of NST to multiple stable Tweedie models and corresponding problems are presented. Copyright Sociedad de Estadística e Investigación Operativa 2014

Suggested Citation

  • 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.
  • Handle: RePEc:spr:testjl:v:23:y:2014:i:3:p:585-606
    DOI: 10.1007/s11749-014-0363-9
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    References listed on IDEAS

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    1. Kokonendji, Célestin C. & Khoudar, Mohamed, 2006. "On Lévy measures for infinitely divisible natural exponential families," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1364-1368, July.
    2. Koudou, A. E. & Pommeret, D., 2002. "A Characterization of Poisson-Gaussian Families by Convolution-Stability," Journal of Multivariate Analysis, Elsevier, vol. 81(1), pages 120-127, April.
    3. Consonni, Guido & Veronese, Piero & Gutiérrez-Peña, Eduardo, 2004. "Reference priors for exponential families with simple quadratic variance function," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 335-364, February.
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    Cited by:

    1. Farouk Mselmi, 2022. "Generalized linear model for subordinated Lévy processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 772-801, June.
    2. 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.
    3. Johann Cuenin & Bent Jørgensen & Célestin C. Kokonendji, 2016. "Simulations of full multivariate Tweedie with flexible dependence structure," Computational Statistics, Springer, vol. 31(4), pages 1477-1492, December.

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