Fisher dispersion index for multivariate count distributions: A review and a new proposal

Aerts, 2017, Robust asymptotic tests for the equality of multivariate coefficients of variation, TEST, 26, 163, 10.1007/s11749-016-0504-4 Aerts, 2015, Multivariate coefficients of variation: Comparison and influence functions, J. Multivariate Anal., 142, 183, 10.1016/j.jmva.2015.08.006 Albert, 2010, A novel definition of the multivariate coefficient of variation, Biom. J., 52, 667, 10.1002/bimj.201000030 Berkhout, 2004, A bivariate Poisson count data model using conditional probabilities, Statist. Neerlandica, 58, 349, 10.1111/j.1467-9574.2004.00126.x Best, 1997, Crockett’s test of fit for the bivariate Poisson, Biom. J., 39, 423, 10.1002/bimj.4710390404 Bonat, 2016, Multivariate covariance generalized linear models, J. Roy. Statist. Soc. Ser. C, 65, 649, 10.1111/rssc.12145 Bonat, 2017, Modelling the covariance structure in multivariate count models: Hunting in Bioko Island, J. Agric. Biol. Environ. Stat., 22, 446, 10.1007/s13253-017-0284-7 Cameron, 1998 Casalis, 1996, The 2d+4 simple quadratic natural exponential families on Rd, Ann. Statist., 24, 1828, 10.1214/aos/1032298298 Chan, 2014, Multivariate generalized Poisson geometric process model with scale mixtures of normal distributions, J. Multivariate Anal., 127, 72, 10.1016/j.jmva.2014.02.002 Cramér, 1974 Crockett, 1979, A quick test of fit of a bivariate distribution, 185 Cuenin, 2016, Simulations of full multivariate Tweedie with flexible dependence structure, Comput. Statist., 31, 1477, 10.1007/s00180-015-0617-3 N. Fernández, L. Fraile, R. Pena, P. Puig, J. Estany, J. Valls, A statistical approach to predict disease outbreaks using reproduction records of sows, 2017. submitted for publication. Ferrari, 2007, Exponential families of mixed Poisson distributions, J. Multivariate Anal., 98, 1283, 10.1016/j.jmva.2006.03.005 Fisher, 1934, The effects of methods of ascertainment upon the estimation of frequencies, Ann. Eugenics, 6, 13, 10.1111/j.1469-1809.1934.tb02105.x Holgate, 1964, Estimation for the bivariate Poisson distribution, Biometrika, 51, 241, 10.1093/biomet/51.1-2.241 Holgate, 1966, Bivariate generalizations of Neyman’s type A distribution, Biometrika, 53, 241, 10.1093/biomet/53.1-2.241 Horn, 1985 Iliopoulos, 2008, UMVU estimation of the ratio of powers of normal generalized variances under correlation, J. Multivariate Anal., 99, 1051, 10.1016/j.jmva.2007.06.008 Inouye, 2017, A review of multivariate distributions for count data derived from the Poisson distribution, WIREs Comput. Statist., 9, 10.1002/wics.1398 Johnson, 1997 Johnson, 2007 Jørgensen, 2016, Discrete dispersion models and their Tweedie asymptotics, AStA Adv. Stat. Anal., 100, 133, 10.1007/s10182-015-0250-z Karlis, 2005, Multivariate Poisson regression with covariance structure, Statist. Comput., 15, 255, 10.1007/s11222-005-4069-4 Karlis, 2005, Mixed Poisson distribution, Internat. Statist. Rev., 73, 35, 10.1111/j.1751-5823.2005.tb00250.x Kokonendji, 2014, Over- and underdispersion models, 506 Kokonendji, 2008, Connections of the Poisson weight function to overdispersion and underdispersion, J. Statist. Plann. Inference, 138, 1287, 10.1016/j.jspi.2007.05.028 Kokonendji, 2007, Comparing UMVU and ML estimators of the generalized variance for natural exponential families, Statistics, 41, 547, 10.1080/02331880701442700 Kokonendji, 2009, Semiparametric estimation for count data through weighted distributions, J. Statist. Plann. Inference, 139, 3625, 10.1016/j.jspi.2009.04.013 Kokonendji, 1996, On the determinant of the second derivative of a Laplace transform, Ann. Statist., 24, 1813, 10.1214/aos/1032298297 Kotz, 2000 Lakshminarayana, 1999, On a bivariate Poisson distribution, Comm. Statist. Theory Methods, 28, 267, 10.1080/03610929908832297 Löwner, 1934, Über monotone Matrixfunktionen, Math. Z., 38, 177, 10.1007/BF01170633 Marshall, 1985, A family of bivariate distributions generated by the bivariate Bernoulli distribution, J. Amer. Statist. Assoc., 80, 332, 10.1080/01621459.1985.10478116 Mellinger, 1965, A mathematical model with application to a study of accident repeatedness among children, J. Amer. Statist. Assoc., 60, 1046, 10.1080/01621459.1965.10480849 Minkova, 2014, Type II bivariate Pólya–Aeppli distribution, Statist. Probab. Lett., 88, 40, 10.1016/j.spl.2014.01.027 Mizère, 2006, Quelques tests de la loi de Poisson contre des alternatives générales basés sur l’indice de dispersion de Fisher, Rev. Stat. Appl., 54, 61 Pedeli, 2013, Some properties of multivariate INAR(1) processes, Comput. Statist. Data Anal., 67, 213, 10.1016/j.csda.2013.05.019 Pfeifer, 2004, Modeling and generating dependent risk processes for IRM and DFA, Astin Bull., 34, 333, 10.1017/S0515036100013726 Puig, 2018, Non-parametric estimation of the number of zeros in truncated count distributions, Scand. J. Stat., 10.1111/sjos.12293 R Core Team, R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, 2016. Reyment, 1960, Studies on nigerian upper cretaceous and lower tertiary ostracoda: Part 1. Senonian and maastrichtian ostracoda, 1 Saghir, 2014, Control chart for monitoring multivariate COM-Poisson attributes, J. Appl. Stat., 41, 200, 10.1080/02664763.2013.838666 Satish, 2014, Predicting intraday trading volume and volume percentages, J. Trading, 9, 15, 10.3905/jot.2014.9.3.015 Serfling, 1980 P. Su, Generation of Multivariate Data with Arbitrary Marginals: Package NORTARA, 2015. https://cran.r-project.org/web/packages/NORTARA/. Sunecher, 2017, A GQL estimation approach for analysing non-stationary over-dispersed BINAR(1) time series, J. Stat. Comput. Simul., 87, 1911, 10.1080/00949655.2017.1296152 van Valen, 1974, Multivariate structural statistics in natural history, J. Theoret. Biol., 45, 235, 10.1016/0022-5193(74)90053-8 Voinov, 1996 Weiß, 2018, Testing for zero inflation and overdispersion in INAR(1) models, Statist. Papers