Baíllo, A.; Berrendero, J. R.; Cárcamo, J. Tests for zero-inflation and overdispersion: a new approach based on the stochastic convex order. (English) Zbl 1453.62034 Comput. Stat. Data Anal. 53, No. 7, 2628-2639 (2009). Summary: A new methodology to detect zero-inflation and overdispersion is proposed, based on a comparison of the expected sample extremes among convexly ordered distributions. The method is very flexible and includes tests for the proportion of structural zeros in zero-inflated models, tests to distinguish between two ordered parametric families and a new general test to detect overdispersion. The performance of the proposed tests is evaluated via some simulation studies. For the well-known fetal lamb data, the conclusion is that the zero-inflated Poisson model should be rejected against other more disperse models, but the negative binomial model cannot be rejected. Cited in 5 Documents MSC: 62-08 Computational methods for problems pertaining to statistics 62F03 Parametric hypothesis testing PDFBibTeX XMLCite \textit{A. Baíllo} et al., Comput. Stat. Data Anal. 53, No. 7, 2628--2639 (2009; Zbl 1453.62034) Full Text: DOI Link References: [1] Aban, I. B.; Cutter, G. R.; Mavinga, N., Inferences and power analysis concerning two negative binomial distributions with an application to MRI lesion counts data, Computational Statistics and Data Analysis, 53, 820-833 (2009) · Zbl 1452.62024 [2] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1965), Dover: Dover New York [3] Böhning, D.; Schlattmann, P.; Lindsay, B., Computer-assisted analysis of mixtures (C.A.MAN): Statistical algorithms, Biometrics, 48, 283-303 (1992) [4] Böhning, D.; Dietz, E.; Schlattmann, P., The zero-inflated Poisson model and the decayed missing and filled teeth index in dental epidemiology, Journal of the Royal Statistical Society Series A, 162, 195-209 (1999) [5] Campbell, M. J.; Machin, D.; Darcangues, C., Coping with extra-Poisson variability in the analysis of factors influencing vaginal ring expulsions, Statistics in Medicine, 10, 241-251 (1991) [6] de la Cal, J.; Cárcamo, J., Inequalities for expected extreme order statistics, Statistics and Probability Letters, 73, 219-231 (2005) · Zbl 1074.60024 [7] Douglas, J. B., Empirical fitting of discrete distributions, Biometrics, 50, 576-579 (1994) [8] El-Shaarawi, A., Some goodness-of-fit methods for the Poisson plus added zero distribution, Applied and Environmental Microbiology, 49, 1304-1306 (1985) [9] Gupta, P. L.; Gupta, R. C.; Tripathi, R. C., Analysis of zero-adjusted count data, Computational Statistics and Data Analysis, 23, 207-218 (1996) · Zbl 0875.62096 [10] He., B.; Gupta, P. L.; Xie, M.; Goh, T. N., A confidence interval test for testing Poisson model against zero-inflated Poisson model, Journal of Applied Statistical Science, 12, 209-220 (2003) · Zbl 1059.62016 [11] Jansakul, N.; Hinde, J. P., Score tests for zero-inflated Poisson models, Computational Statistics and Data Analysis, 40, 75-96 (2002) · Zbl 0993.62013 [12] Johnson, N. L.; Kemp, A. W.; Kotz, S., Univariate Discrete Distributions (2005), Wiley: Wiley New York · Zbl 1092.62010 [13] Leroux, B. G.; Puterman, M. L., Maximum-penalized-likelihood estimation for independent and Markov-dependent mixture models, Biometrics, 48, 545-558 (1992) [14] Nie, L.; Wu., G.; Brockman, F. J.; Zhang, W., Integrated analysis of transcriptomic and proteomic data of Desulfovibrio vulgaris: Zero-inflated Poisson regression models to predict abundance of undetected proteins, Bioinformatics, 22, 1641-1647 (2006) [15] Ridout, M.; Hinde, J.; Demétrio, C., A score test for testing a zero-infalted Poisson regression model against zero-inflated negative binomial alternatives, Biometrics, 57, 219-223 (2001) · Zbl 1209.62079 [16] Rigby, R. A.; Stasinopoulos, D. M.; Akantziliotou, C., A framework for modelling overdispersed count data including the Poisson-shifted generalized inverse Gaussian distribution, Computational Statistics and Data Analysis, 53, 381-393 (2008) · Zbl 1231.62019 [17] Shaked, M.; Shanthikumar, J. G., Stochastic Orders (2007), Springer: Springer New York [18] Thas, O.; Rayner, J. C.W., Smooth test for the zero-inflated Poisson distribution, Biometrics, 61, 808-815 (2005) · Zbl 1078.62015 [19] van den Broek, J., A score test for zero inflation in a Poisson distribution, Biometrics, 51, 738-743 (1995) · Zbl 0825.62377 [20] van den Vaart, A. W., Asymptotic Statistics (1998), University Press: University Press Cambridge · Zbl 0910.62001 [21] Xie, M.; He, B.; Goh, T. N., Zero-inflated Poisson model in statistical process control, Computational Statistics and Data Analysis, 38, 191-201 (2001) · Zbl 1095.62517 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.