Discrete dispersion models and their Tweedie asymptotics

Bent Jørgensen1, Célestin C. Kokonendji2
1 University of Southern Denmark
2Laboratoire de Mathématiques de Besançon-UMR 6623 CNRS, Université de Franche-Comté-UFR Sciences et Techniques, Besançon cedex, France

Tóm tắt

Từ khóa


Tài liệu tham khảo

Barreto-Souza, W., Bourguignon, M.: A skew INAR(1) process on $$\mathbb{Z}$$ Z . AStA Adv. Stat. Anal. 99, 189–208 (2015)

Bryc, W.: Free exponential families as kernel families. Demonstr. Math. XLII, 657–672 (2009)

Dobbie, M.J., Welsh, A.H.: Models for zero-inflated count data using the Neyman type A distribution. Stat. Model. 1, 65–80 (2001)

El-Shaarawi, A.H., Zhu, R., Joe, H.: Modelling species abundance using the Poisson-Tweedie family. Environmetrics 22, 152–164 (2011)

Giles, D.E.: Hermite regression analysis of multi-modal count data. Econ. Bull. 30, 2936–2945 (2010)

Grandell, J.: Mixed Poisson Processes. Chapman & Hall, London (1997)

Harremoës, P., Johnson, O., Kontoyiannis, I.: Thinning, entropy, and the law of thin numbers. IEEE Trans. Inf. Theory 56, 4228–4244 (2010)

Hougaard, P., Lee, M-L.T., Whitmore, G.A.: Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes. Biometrics 53, 1225–1238 (1997)

Jensen, S.T., Nielsen, B.: On convergence of multivariate Laplace transforms. Statist. Probab. Lett. 33, 125–128 (1997)

Johnson, N.L., Kotz, S., Balakrishnan, N.: Discrete Multivariate Distributions. Wiley, New York (1997)

Johnson, N.L., Kemp, A.W., Kotz, S.: Univariate Discrete Distributions, 3rd edn. Wiley, Hoboken (2005)

Jørgensen, B.: The Theory of Dispersion Models. Chapman & Hall, London (1997)

Jørgensen, B., Kokonendji, C.C.: Dispersion models for geometric sums. Braz. J. Probab. Statist. 25, 263–293 (2011)

Jørgensen, B., Martínez, J.R.: Multivariate exponential dispersion models. In: Kollo, T. (ed.) Multivariate Statistics: Theory and Applications. Proceedings of the IX Tartu Conference on Multivariate Statistics & XX International Workshop on Matrices and Statistics, pp. 73–98. World Scientific, Singapore (2013)

Jørgensen, B., Martínez, J.R., Tsao, M.: Asymptotic behaviour of the variance function. Scand. J. Stat. 21, 223–243 (1994)

Jørgensen, B., Goegebeur, Y., Martínez, J.R.: Dispersion models for extremes. Extremes 13, 399–437 (2010)

Jørgensen, B., Demétrio, C.G.B., Kristensen, E., Banta, G.T., Petersen, H.C., Delefosse, M.: Bias-corrected Pearson estimating functions for Taylor’s power law applied to benthic macrofauna data. Stat. Probab. Lett. 81, 749–758 (2011)

Kalashnikov, V.: Geometric Sums: Bounds for Rare Events with Applications. Kluwer Academic Publishers, Dordrecht (1997)

Karlis, D., Xekalaki, E.: Mixed poisson distributions. Int. Stat. Rev. 73, 35–58 (2005)

Kemp, A.W.: Characterizations of a discrete normal distribution. J. Stat. Plan. Inf. 63, 223–229 (1997)

Kemp, C.D., Kemp, A.W.: Some properties of the ‘Hermite’ distribution. Biometrika 52, 381–394 (1965)

Khatri, C.G.: On certain properties of power-series distributions. Biometrika 46, 486–490 (1959)

Kokonendji, C.C., Pérez-Casany, M.: A note on weighted count distributions. J. Stat. Theory Appl. 11, 337–352 (2012)

Kokonendji, C.C., Dossou-Gbété, S., Demétrio, C.G.B.: Some discrete exponential dispersion models: Poisson-Tweedie and Hinde-Demétrio classes. Stat Operat Res Trans (SORT) 28, 201–214 (2004)

Kokonendji, C.C., Mizère, D., Balakrishnan, N.: Connections of the Poisson weight function to overdispersion and underdispersion. J. Stat. Plan. Inf. 138, 1287–1296 (2008)

Massé, J.-C., Theodorescu, R.: Neyman type A distribution revisited. Stat. Neerl. 59, 206–213 (2005)

McKenzie, E.: Some simple models for discrete variates time series. Water Resour. Bull. 21, 645–650 (1985)

Mora, M.: La convergence des fonctions variance des familles exponentielles naturelles. Ann. Fac. Sci. Toulouse 11(5), 105–120 (1990)

Pistone, G., Wynn, H.P.: Finitely generated cumulants. Stat. Sinica 9, 1029–1052 (1999)

Puig, P.: Characterizing additively closed discrete models by a property of their maximum likelihood estimators, with an application to generalized Hermite distributions. J. Am. Stat. Assoc. 98, 687–692 (2003)

Puig, P., Barquinero, F.: An application of compound Poisson modelling to biological dosimetry. Proc. R. Soc. A 467, 897–910 (2011)

Puig, P., Valero, J.: Count data distributions: some characterizations with applications. J. Am. Stat. Assoc. 101, 332–340 (2006)

Puig, P., Valero, J.: Characterization of count data distributions involving additivity and binomial subsampling. Bernoulli 13, 544–555 (2007)

Ristić, M.M., Bakouch, H.S., Nastić, A.S.: A new geometric first-order integer-valued autoregressive (NGINAR(1)) process. J. Stat. Plan. Inference 139, 2218–2226 (2009)

Roy, D.: The discrete normal distribution. Commun. Stat. Theory Methods 32, 1871–1883 (2003)

Rudin, W.: Principles of Mathematical Analysis, 3rd edn. McGraw-Hill, New York (1976)

Sellers, K.F., Borle, S., Shmueli, G.: The COM-Poisson model for count data: a survey of methods and applications. Appl. Stoch. Models Bus. Ind. 28, 104–116 (2012)

Shmueli, G., Minka, T.P., Kadane, J.P., Borle, S., Boatwright, P.: A useful distribution for fitting discrete data: revival of the Conway-Maxwell-Poisson distribution. Appl. Stat. 54, 127–142 (2005)

Steutel, F.W., van Harn, K.: Discrete analogues of self-decomposability and stability. Ann. Probab. 7, 893–899 (1979)

Taylor, L.R., Taylor, R.A.J.: Aggregation, migration and population mechanics. Nature 265, 415–421 (1977)

Thedéen, T.: The inverses of thinned point processes. Research report 1986:1. Department of Statistics, University of Stockholm (1986)

Tweedie, M.C.K.: An index which distinguishes between some important exponential families. In: Ghosh, J.K., Roy, J. (eds.) Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, pp. 579–604. Indian Statistical Institute, Calcutta (1984)

Weiß, C.H.: Thinning operations for modeling time series of counts—a survey. AStA Adv. Stat. Anal. 92, 319–341 (2008)

Willmot, G.E.: The Poisson-inverse Gaussian distribution as an alternative to the negative binomial. Scand. Actuar. J. 1987, 113–127 (1987)

Wimmer, G., Altmann, G.: Thesaurus of Univariate Discrete Probability Distributions. STAMM Verlag, Essen (1999)

Wiuf, C., Stumpf, M.P.H.: Binomial subsampling. Proc. R. Soc. A 462, 1181–1195 (2006)