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References

Published online by Cambridge University Press:  02 March 2023

Kimberly F. Sellers
Kimberly F. Sellers
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Georgetown University, Washington DC
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The Conway–Maxwell–Poisson Distribution , pp. 312 - 326
Publisher: Cambridge University Press
Print publication year: 2023

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References

Abbas, N., Riaz, M., and Does, R. J. M. M. (2013). Mixed exponentially weighted moving average–cumulative sum charts for process monitoring. Quality and Reliability Engineering International, 29(3):345–356.Google Scholar
Abbasi, S. A. (2017). Poisson progressive mean control chart. Quality and Reliability Engineering International, 33(8):1855–1859.Google Scholar
Adamidis, K. and Loukas, S. (1998). A lifetime distribution with decreasing failure rate. Statistics & Probability Letters, 39(1):35–42.Google Scholar
Ahrens, J. H. and Dieter, U. (1982). Computer generation of Poisson deviates from modified normal distributions. ACM Transactions on Mathematical Software, 8(2): 163–179.Google Scholar
Airoldi, E. M., Anderson, A. G., Fienberg, S. E., and Skinner, K. K. (2006). Who wrote Ronald Reagan’s radio addresses? Bayesian Analysis, 1(2):289–319.Google Scholar
Al-Osh, M. A. and Alzaid, A. A. (1987). First-order integer valued autoregressive (INAR(1)) process. Journal of Time Series Analysis, 8(3):261–275.Google Scholar
Al-Osh, M. A. and Alzaid, A. A. (1988). Integer-valued moving average (INMA) process. Statistical Papers, 29(1):281–300.Google Scholar
Al-Osh, M. A. and Alzaid, A. A. (1991). Binomial autoregressive moving average models. Communications in Statistics. Stochastic Models, 7(2):261–282.Google Scholar
Albers, W. (2011). Control charts for health care monitoring under overdispersion. Metrika, 74:67–83.Google Scholar
Alevizakos, V. and Koukouvinos, C. (2019). A double exponentially weighted moving average control chart for monitoring COM–Poisson attributes. Quality and Reliability Engineering International, 35(7):2130–2151.Google Scholar
Alevizakos, V. and Koukouvinos, C. (2022). A progressive mean control chart for COM–Poisson distribution. Communications in Statistics – Simulation and Computation, 51(3):849–867.Google Scholar
Alqawba, M. and Diawara, N. (2021). Copula-based Markov zero-inflated count time series models with application. Journal of Applied Statistics, 48(5):786–803.Google Scholar
Alzaid, A. A. and Al-Osh, M. A. (1993). Some autoregressive moving average processes with generalized Poisson marginal distributions. Annals of the Institute of Statistical Mathematics, 45(2):223–232.Google Scholar
Anan, O., Böhning, D., and Maruotti, A. (2017). Population size estimation and heterogeneity in capture–recapture data: A linear regression estimator based on the Conway–Maxwell–Poisson distribution. Statistical Methods & Applications, 26(1):49–79.Google Scholar
Arab, A. (2015). Spatial and spatio-temporal models for modeling epidemiological data with excess zeros. International Journal of Environmental Research and Public Health, 12(9):10536–10548.CrossRefGoogle ScholarPubMed
Arbous, A. and Kerrick, J. E. (1951). Accident statistics and the concept of accident proneness. Biometrics, 7(4):340–432.Google Scholar
Aslam, M., Ahmad, L., Jun, C. H., and Arif, O. H. (2016a). A control chart for COM– Poisson distribution using multiple dependent state sampling. Quality and Reliability Engineering International, 32(8):2803–2812.Google Scholar
Aslam, M., Azam, M., and Jun, C.-H. (2016b). A control chart for COM–Poisson distribution using resampling and exponentially weighted moving average. Quality and Reliability Engineering International, 32(2):727–735.Google Scholar
Aslam, M., Khan, N., and Jun, C.-H. (2018). A hybrid exponentially weighted moving average chart for COM–Poisson distribution. Transactions of the Institute of Measurement and Control, 40(2):456–461.Google Scholar
Aslam, M., Saghir, A., Ahmad, L., Jun, C.-H., and Hussain, J. (2017). A control chart for COM–Poisson distribution using a modified EWMA statistic. Journal of Statistical Computation and Simulation, 87(18):3491–3502.Google Scholar
Atkinson, A. C. and Yeh, L. (1982). Inference for Sichel’s compound Poisson distribution. Journal of the American Statistical Association, 77(377):153–158.Google Scholar
Bailey, B. J. R. (1990). A model for function word counts. Journal of the Royal Statistical Society. Series C (Applied Statistics), 39(1):107–114.Google Scholar
Balakrishnan, N., Barui, S., and Milienos, F. (2017). Proportional hazards under Conway–Maxwell–Poisson cure rate model and associated inference. Statistical Methods in Medical Research, 26(5):2055–2077.CrossRefGoogle ScholarPubMed
Balakrishnan, N. and Feng, T. (2018). Proportional odds under Conway–Maxwell– Poisson cure rate model and associated likelihood inference. Statistics, Optimization & Information Computing, 6(3):305–334.Google Scholar
Balakrishnan, N. and Pal, S. (2012). EM algorithm-based likelihood estimation for some cure rate models. Journal of Statistical Theory and Practice, 6(4): 698–724.Google Scholar
Balakrishnan, N. and Pal, S. (2013). Lognormal lifetimes and likelihood-based inference for flexible cure rate models based on COM–Poisson family. Computational Statistics and Data Analysis, 67:41–67.Google Scholar
Balakrishnan, N. and Pal, S. (2015a). An EM algorithm for the estimation of parameters of a flexible cure rate model with generalized gamma lifetime and model discrimination using likelihood- and information-based methods. Computational Statistics, 30(1):151–189.Google Scholar
Balakrishnan, N. and Pal, S. (2015b). Likelihood inference for flexible cure rate models with gamma lifetimes. Communications in Statistics – Theory and Methods, 44(19):4007–4048.Google Scholar
Balakrishnan, N. and Pal, S. (2016). Expectation maximization-based likelihood inference for flexible cure rate models with Weibull lifetimes. Statistical Methods in Medical Research, 25(4):1535–1563.Google Scholar
Banerjee, S. and Carlin, B. P. (2004). Parametric spatial cure rate models for interval- censored time-to-relapse data. Biometrics, 60(1):268–275.Google Scholar
Barlow, R. and Proschan, F. (1965). Mathematical Theory of Reliability. Classics in Applied Mathematics, 17. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA. Republished in 1996.Google Scholar
Barriga, G. D. and Louzada, F. (2014). The zero-inflated Conway–Maxwell–Poisson distribution: Bayesian inference, regression modeling and influence diagnostic. Statistical Methodology, 21:23–34.Google Scholar
Bates, D., Mächler, M., Bolker, B., and Walker, S. (2015). Fitting linear mixed-effects models using lme4. Journal of Statistical Software, 67(1):1–48.CrossRefGoogle Scholar
Benjamin, M. A., Rigby, R. A., and Stasinopoulos, D. M. (2003). Generalized autoregressive moving average models. Journal of the American Statistical Association, 98(461):214–223.Google Scholar
Bennett, S. (1983). Log-logistic regression models for survival data. Journal of the Royal Statistical Society. Series C (Applied Statistics), 32(2):165–171.Google Scholar
Benson, A. and Friel, N. (2017). Bayesian inference, model selection and likelihood estimation using fast rejection sampling: The Conway–Maxwell–Poisson distribution. Bayesian Analysis, 16(3):905–931.Google Scholar
Berkson, J. and Gage, R. P. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47(259):501–515.Google Scholar
Blocker, A. W. (2018). fastGHQuad: Fast Rcpp implementation of Gauss-Hermite quadrature, version 1.0. https://cran.r-project.org/web/packages/fastGHQuad/ index.html.Google Scholar
Boag, J. W. (1949). Maximum likelihood estimates of the proportion of patients cured by cancer therapy. Journal of the Royal Statistical Society. Series B (Methodological), 11(1):15–53.Google Scholar
Boatwright, P., Borle, S., and Kadane, J. B. (2003). A model of the joint distribution of purchase quantity and timing. Journal of the American Statistical Association, 98(463):564–572.Google Scholar
Booth, J. G., Casella, G., Friedl, H., and Hobert, J. P. (2003). Negative binomial loglinear mixed models. Statistical Modelling, 3(3):179–191.Google Scholar
Borges, P., Rodrigues, J., Balakrishnan, N., and Bazán, J. (2014). A COM–Poisson type generalization of the binomial distribution and its properties and applications. Statistics and Probability Letters, 87(1):158–166.Google Scholar
Borle, S., Boatwright, P., and Kadane, J. B. (2006). The timing of bid placement and extent of multiple bidding: An empirical investigation using eBay online auctions. Statistical Science, 21(2):194–205.Google Scholar
Borle, S., Boatwright, P., Kadane, J. B., Nunes, J. C., and Shmueli, G. (2005). The effect of product assortment changes on customer retention. Marketing Science, 24(4):616–622.Google Scholar
Borle, S., Dholakia, U., Singh, S., and Westbrook, R. (2007). The impact of survey participation on subsequent behavior: An empirical investigation. Marketing Science, 26(5):711–726.Google Scholar
Borror, C. M., Champ, C. W., and Rigdon, S. E. (1998). Poisson EWMA control charts. Journal of Quality Technology, 30(4):352–361.Google Scholar
Bourke, P. D. (2001). The geometric CUSUM chart with sampling inspection for monitoring fraction defective. Journal of Applied Statistics, 28(8):951–972.Google Scholar
Brännäs, K. and Hall, A. (2001). Estimation in integer-valued moving average models. Applied Stochastic Models in Business and Industry, 17(3):277–291.Google Scholar
Brännäs, K. J. (2001). Generalized integer-valued autoregression. Econometric Reviews, 20(4):425–443.Google Scholar
Breslow, N. E. (1984). Extra-Poisson variation in log-linear models. Journal of the Royal Statistical Society. Series C (Applied Statistics), 33(1):38–44.Google Scholar
Brook, D. and Evans, D. A. (1972). An approach to the probability distribution of CUSUM run length. Biometrika, 59(3):539–549.Google Scholar
Brooks, M. E., Kristensen, K., van Benthem, K. J., Magnusson, A., Berg, C. W., Nielsen, A., Skaug, H. J., Mächler, M., and Bolker, B. M. (2017). glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. The R Journal, 9(2):378–400.Google Scholar
Brown, T. C. and Xia, A. (2001). Stein’s method and birth-death processes. Annals of Probability, 29(3):1373–1403.Google Scholar
Burnham, K. P. and Anderson, D. R. (2002). Model Selection and Multimodel Inference. Springer.Google Scholar
Cancho, V., de Castro, M., and Rodrigues, J. (2012). A Bayesian analysis of the Conway–Maxwell–Poisson cure rate model. Stat Papers, 53(1): 165–176.Google Scholar
Canty, A. and Ripley, B. D. (2020). boot: Bootstrap R (S-Plus) Functions. R package version 1.3-25.Google Scholar
Casella, G. and Berger, R. L. (1990). Statistical Inference. Duxbury Press, Belmont, California.Google Scholar
Çinlar, E. (1975). Introduction to Stochastic Processes. Prentice-Hall.Google Scholar
Chakraborty, S. and Imoto, T. (2016). Extended Conway–Maxwell–Poisson distribution and its properties and applications. Journal of Statistical Distributions and Applications, 3(5):1–19.Google Scholar
Chakraborty, S. and Ong, S. H. (2016). A COM–Poisson-type generalization of the negative binomial distribution. Communications in Statistics – Theory and Methods, 45(14):4117–4135.Google Scholar
Chanialidis, C. (2020). combayes: Bayesian regression for COM–Poisson data. version 0.0.1.Google Scholar
Chanialidis, C., Evers, L., Neocleous, T., and Nobile, A. (2014). Retrospective sampling in MCMC with an application to COM–Poisson regression. Stat, 3(1): 273–290.Google Scholar
Chanialidis, C., Evers, L., Neocleous, T., and Nobile, A. (2017). Efficient Bayesian inference for COM–Poisson regression models. Statistics and Computing, 28(3): 595–608.Google Scholar
Chatla, S. B. and Shmueli, G. (2018). Efficient estimation of COM–Poisson regression and a generalized additive model. Computational Statistics and Data Analysis, 121:71–88.Google Scholar
Chen, J.-H. (2020). A double generally weighted moving average chart for monitoring the COM–Poisson processes. Symmetry, 12(6):1014.Google Scholar
Chen, M.-H., Ibrahim, J. G., and Sinha, D. (1999). A new Bayesian model for survival data with a surviving fraction. Journal of the American Statistical Association, 94(447):909–919.Google Scholar
Chen, N., Zhou, S., Chang, T.-S., and Huang, H. (2008). Attribute control charts using generalized zero-inflated Poisson distribution. Quality and Reliability Engineering International, 24(7):793–806.Google Scholar
Chiu, W.-C. and Lu, S.-L. (2015). On the steady-state performance of the Poisson double GWMA control chart. Quality Technology & Quantitative Management, 12(2):195–208.Google Scholar
Chiu, W.-C. and Sheu, S.-H. (2008). Fast initial response features for Poisson GWMA control charts. Communications in Statistics – Simulation and Computation, 37(7):1422–1439.CrossRefGoogle Scholar
Choo-Wosoba, H. and Datta, S. (2018). Analyzing clustered count data with a cluster- specific random effect zero-inflated Conway–Maxwell–Poisson distribution. Journal of Applied Statistics, 45(5):799–814.Google Scholar
Choo-Wosoba, H., Gaskins, J., Levy, S., and Datta, S. (2018). A Bayesian approach for analyzing zero-inflated clustered count data with dispersion. Statistics in Medicine, 37(5):801–812.Google Scholar
Choo-Wosoba, H., Levy, S. M., and Datta, S. (2016). Marginal regression models for clustered count data based on zero-inflated Conway–Maxwell–Poisson distribution with applications. Biometrics, 72(2):606–618.Google Scholar
Clark, S. J. and Perry, J. N. (1989). Estimation of the negative binomial parameter κ by maximum quasi-likelihood. Biometrics, 45(1):309–316.Google Scholar
Consul, P. and Jain, G. (1973). A generalization of the Poisson distribution. Technometrics, 15(4):791–799.Google Scholar
Consul, P. C. (1988). Generalized Poisson Distributions. CRC Press.Google Scholar
Conway, R. W. and Maxwell, W. L. (1962). A queuing model with state dependent service rates. Journal of Industrial Engineering, 12(2):132–136.Google Scholar
Cordeiro, G. M., Rodrigues, J., and de Castro, M. (2012). The exponential COM– Poisson distribution. Stat Papers, 53(3):653–664.Google Scholar
Curran, J., Williams, A., Kelleher, J., and Barber, D. (2015). The multicool Package: Permutations of Multisets in Cool-Lex Order, 0.1-6 edition.Google Scholar
Daly, F. and Gaunt, R. (2016). The Conway-Maxwell-Poisson distribution: Distributional theory and approximation. Alea: Latin American journal of probability and mathematical statistics, 13(2):635–658.CrossRefGoogle Scholar
De Oliveira, V. (2013). Hierarchical Poisson models for spatial count data. Journal of Multivariate Analysis, 122:393–408.Google Scholar
del Castillo, J. and Pérez-Casany, M. (2005). Overdispersed and underdispersed Poisson generalizations. Journal of Statistical Planning and Inference, 134(2):486–500.Google Scholar
Demirtas, H. (2017). On accurate and precise generation of generalized Poisson variates. Communications in Statistics – Simulation and Computation, 46(1):489–499.Google Scholar
Diggle, P. J. and Milne, R. K. (1983). Negative binomial quadrat counts and point processes. Scandinavian Journal of Statistics, 10(4):257–267.Google Scholar
Dobson, A. J. and Barnett, A. G. (2018). An Introduction to Generalized Linear Models. Chapman & Hall/CRC Press, 4th edition.Google Scholar
Doss, D. C. (1979). Definition and characterization of multivariate negative binomial distribution. Journal of Multivariate Analysis, 9(3):460–464.Google Scholar
Dunn, J. (2012). compoisson: Conway–Maxwell–Poisson distribution, version 0.3. https://cran.r-project.org/web/packages/compoisson/index.html.Google Scholar
Efron, B. (1986). Double exponential families and their use in generalized linear regression. Journal of the American Statistical Association, 81(395):709–721.Google Scholar
Famoye, F. (1993). Restricted generalized Poisson regression model. Communications in Statistics – Theory and Methods, 22(5):1335–1354.Google Scholar
Famoye, F. (2007). Statistical control charts for shifted generalized Poisson distribution. Statistical Methods and Applications, 3(3):339–354.Google Scholar
Famoye, F. (2010). On the bivariate negative binomial regression model. Journal of Applied Statistics, 37(6):969–981.Google Scholar
Famoye, F. and Consul, P. C. (1995). Bivariate generalized Poisson distribution with some applications. Metrika, 42(1):127–138.Google Scholar
Famoye, F. and Singh, K. P. (2006). Zero-inflated generalized Poisson regression model with an application to domestic violence data. Journal of Data Science, 4(1): 117–130.Google Scholar
Famoye, F., Wulu, J. Jr., and Singh, K. P. (2004). On the generalized Poisson regression model with an application to accident data. Journal of Data Science, 2(3): 287–295.Google Scholar
Fang, Y. (2003). C-chart, X-chart, and the Katz family of distributions. Journal of Quality Technology, 35(1):104–114.Google Scholar
Farewell, V. T. (1982). The use of mixture models for the analysis of survival data with long-term survivors. Biometrics, 38(4):1041–1046.Google Scholar
Francis, R. A., Geedipally, S. R., Guikema, S. D., Dhavala, S. S., Lord, D., and LaRocca, S. (2012). Characterizing the performance of the Conway–Maxwell–Poisson generalized linear model. Risk Analysis, 32(1):167–183.Google Scholar
Freeland, R. K. and McCabe, B. (2004). Analysis of low count time series data by Poisson autoregression. Journal of Time Series Analysis, 25(5): 701–722.Google Scholar
Fung, T., Alwan, A., Wishart, J., and Huang, A. (2020). mpcmp: Mean-parametrized Conway–Maxwell–Poisson, version 0.3.6. https://cran.r-project.org/web/packages/ mpcmp/index.html.Google Scholar
Fürth, R. (1918). Statistik und wahrscheinlichkeitsnachwirkung. Physikalische Zeitschrift, 19:421–426.Google Scholar
Gan, F. F. (1990). Monitoring Poisson observations using modified exponentially weighted moving average control charts. Communications in Statistics – Simulation and Computation, 19(1):103–124.Google Scholar
Gaunt, R. E., Iyengar, S., Daalhuis, A. B. O., and Simsek, B. (2016). An asymptotic expansion for the normalizing constant of the Conway–Maxwell–Poisson distribution. arXiv:1612.06618.Google Scholar
Genest, C. and Nešlehová, J. (2007). A primer on copulas for count data. ASTIN Bulletin, 37(2):475–515.Google Scholar
Gilbert, P. and Varadhan, R. (2016). numDeriv: Accurate Numerical Derivatives. R package version 2016.8-1.Google Scholar
Gillispie, S. B. and Green, C. G. (2015). Approximating the Conway–Maxwell–Poisson distribution normalization constant. Statistics, 49(5):1062–1073.Google Scholar
Greene, W. H. (1994). Accounting for Excess Zeros and Sample Selection in Poisson and Negative Binomial Regression Models. SSRN eLibrary.Google Scholar
Guikema, S. D. and Coffelt, J. P. (2008). A flexible count data regression model for risk analysis. Risk Analysis, 28(1):213–223.Google Scholar
Gupta, R. C. (1974). Modified power series distributions and some of its applications. Sankhya Series B, 36:288–298.Google Scholar
Gupta, R. C. (1975). Maximum likelihood estimation of a modified power series distribution and some of its applications. Communications in Statistics – Theory and Methods, 4(7):689–697.Google Scholar
Gupta, R. C. and Huang, J. (2017). The Weibull–Conway–Maxwell–Poisson distribution to analyze survival data. Journal of Computational and Applied Mathematics, 311:171–182.Google Scholar
Gupta, R. C. and Ong, S. (2004). A new generalization of the negative binomial distribution. Computational Statistics & Data Analysis, 45(2):287–300.Google Scholar
Gupta, R. C. and Ong, S. (2005). Analysis of long-tailed count data by Poisson mixtures. Communications in Statistics – Theory and Methods, 34(3):557–573.Google Scholar
Gupta, R. C., Sim, S. Z., and Ong, S. H. (2014). Analysis of discrete data by Conway– Maxwell–Poisson distribution. AStA Advances in Statistical Analysis, 98(4): 327–343.Google Scholar
Guttorp, P. (1995). Stochastic Modeling of Scientific Data. Chapman & Hall/CRC Press.Google Scholar
Hilbe, J. M. (2007). Negative Binomial Regression. Cambridge University Press, 5th edition.Google Scholar
Hilbe, J. M. (2014). Modeling Count Data. Cambridge University Press.Google Scholar
Hinde, J. (1982). Compound Poisson regression models. In Gilchrist, R., editor, GLIM 82: Proc. Internat. Conf. Generalized Linear Models, pages 109–121, Berlin. Springer.Google Scholar
Holgate, P. (1964). Estimation for the bivariate Poisson distribution. Biometrika, 51 (1–2):241–245.Google Scholar
Huang, A. (2017). Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts. Statistical Modelling, 17(6):359–380.Google Scholar
Huang, A. and Kim, A. S. I. (2019). Bayesian Conway–Maxwell–Poisson regression models for overdispersed and underdispersed counts. Communications in Statistics – Theory and Methods, 50(13):1–12.Google Scholar
Hwang, Y., Joo, H., Kim, J.-S., and Kweon, I.-S. (2007). Statistical background subtraction based on the exact per-pixel distributions. In MVA2007 IAPR Conference on Machine Vision Applications, May 16–18, 2007, pages 540–543, Tokyo, Japan.Google Scholar
Imoto, T. (2014). A generalized Conway-Maxwell-Poisson distribution which includes the negative binomial distribution. Applied Mathematics and Computation, 247(C):824–834.Google Scholar
Jackman, S., Tahk, A., Zeileis, A., Maimone, C., Fearon, J., and Meers, Z. (2017). pscl: Political Science Computational Laboratory, version 1.5.2. https://cran.r-project.org/web/packages/pscl/index.html.Google Scholar
Jackson, M. C., Johansen, L., Furlong, C., Colson, A., and Sellers, K. F. (2010). Modelling the effect of climate change on prevalence of malaria in western Africa. Statistica Neerlandica, 64(4):388–400.Google Scholar
Jackson, M. C. and Sellers, K. F. (2008). Simulating discrete spatially correlated Poisson data on a lattice. International Journal of Pure and Applied Mathematics, 46(1): 137–154.Google Scholar
Jiang, R. and Murthy, D. (2011). A study of Weibull shape parameter: Properties and significance. Reliability Engineering & System Safety, 96(12):1619–1626.Google Scholar
Jin-Guan, D. and Yuan, L. (1991). The integer-valued autoregressive (INAR(p)) model. Journal of Time Series Analysis, 12(2):129–142.Google Scholar
Joe, H. (1996). Time series models with univariate margins in the convolution-closed infinitely divisible class. Journal of Applied Probability, 33(3):664–677.Google Scholar
Joe, H. (1997). Multivariate Models and Multivariate Dependence Concepts. Chapman & Hall/CRC Press, 1st edition.Google Scholar
Joe, H. (2014). Dependence Modeling with Copulas. Chapman & Hall/CRC Monographs on Statistics & Applied Probability. CRC Press.Google Scholar
Johnson, N., Kotz, S., and Balakrishnan, N. (1997). Discrete Multivariate Distributions. John Wiley & Sons.Google Scholar
Jowaheer, V., Khan, N. M., and Sunecher, Y. (2018). A BINAR(1) time-series model with cross-correlated COM—Poisson innovations. Communications in Statistics – Theory and Methods, 47(5):1133–1154.Google Scholar
Jowaheer, V. and Mamode Khan, N. A. (2009). Estimating regression effects in COM– Poisson generalized linear model. International Journal of Computational and Mathematical Sciences, 3(4):168–173.Google Scholar
Jung, R. C. and Tremayne, A. R. (2006). Binomial thinning models for integer time series. Statistical Modelling, 6(2):81–96.Google Scholar
Kadane, J. B. (2016). Sums of possibly associated Bernoulli variables: The Conway– Maxwell-Binomial distribution. Bayesian Analysis, 11(2):403–420.Google Scholar
Kadane, J. B., Krishnan, R., and Shmueli, G. (2006a). A data disclosure policy for count data based on the COM–Poisson distribution. Management Science, 52(10): 1610–1617.Google Scholar
Kadane, J. B., Shmueli, G., Minka, T. P., Borle, S., and Boatwright, P. (2006b). Conjugate analysis of the Conway–Maxwell–Poisson distribution. Bayesian Analysis, 1(2):363–374.Google Scholar
Kadane, J. B. and Wang, Z. (2018). Sums of possibly associated multivariate indicator functions: The Conway–Maxwell-multinomial distribution. Brazilian Journal of Probability and Statistics, 32(3):583–596.Google Scholar
Kaminsky, F. C., Benneyan, J. C., Davis, R. D., and Burke, R. J. (1992). Statistical control charts based on a geometric distribution. Journal of Quality Technology, 24(2):63–69.Google Scholar
Kannan, D. (1979). An Introduction to Stochastic Processes. Elsevier North Holland.Google Scholar
Karlis, D. and Ntzoufras, I. (2005). The bivpois package: Bivariate Poisson models using the EM algorithm, 0.50-2 edition.Google Scholar
Karlis, D. and Ntzoufras, I. (2008). Bayesian modelling of football outcomes: Using the Skellam’s distribution for the goal difference. IMA Journal of Management Mathematics, 20(2):133–145.Google Scholar
Kemp, C. D. and Kemp, A. W. (1956). Generalized hypergeometric distributions. Journal of the Royal Statistical Society Series B, 18(2):202–211.Google Scholar
Khan, N. M. and Jowaheer, V. (2013). Comparing joint GQL estimation and GMM adaptive estimation in COM–Poisson longitudinal regression model. Communications in Statistics – Simulation and Computation, 42(4):755–770.Google Scholar
Khan, N. M., Sunecher, Y., and Jowaheer, V. (2016). Modelling a non-stationary BINAR(1) Poisson process. Journal of Statistical Computation and Simulation, 86(15):3106–3126.Google Scholar
Kim, Y. J. and Jhun, M. (2008). Cure rate model with interval censored data. Statistics in Medicine, 27(1):3–14.Google Scholar
Kocherlakota, S. and Kocherlakota, K. (1992). Bivariate Discrete Distributions. Marcel Dekker.Google Scholar
Kokonendji, C. C. (2014). Over-and underdispersion models. In Balakrishnan, N., editor, Methods and Applications of Statistics in Clinical Trials: Planning, Analysis, and Inferential Methods, pages 506–526. John Wiley & Sons.Google Scholar
Kokonendji, C. C., Mizere, D., and Balakrishnan, N. (2008). Connections of the Poisson weight function to overdispersion and underdispersion. Journal of Statistical Planning and Inference, 138(5):1287–1296.Google Scholar
Kokonendji, C. C. and Puig, P. (2018). Fisher dispersion index for multivariate count distributions: A review and a new proposal. Journal of Multivariate Analysis, 165(C):180–193.Google Scholar
Krishnamoorthy, A. S. (1951). Multivariate binomial and Poisson distributions. Sankhyā: The Indian Journal of Statistics (1933–1960), 11(2):117–124.Google Scholar
Kuş, C. (2007). A new lifetime distribution. Computational Statistics and Data Analysis, 51(9):4497–4509.Google Scholar
Kutner, M. H., Nachtsheim, C. J., and Neter, J. (2003). Applied Linear Regression Models, 4th edition. McGraw-Hill.Google Scholar
Lambert, D. (1992). Zero-inflated Poisson regression, with an application to defects in manufacturing. Technometrics, 34(1):1–14.Google Scholar
Lange, K. (1995). A gradient algorithm locally equivalent to the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological), 57(2):425–437.Google Scholar
Lee, J., Wang, N., Xu, L., Schuh, A., and Woodall, H. W. (2013). The effect of parameter estimation on upper-sided Bernoulli cumulative sum charts. Quality and Reliability Engineering International, 29(5):639–651.Google Scholar
Lee, M.-L. T. (1996). Properties and applications of the Sarmanov family of bivariate distributions. Communications in Statistics – Theory and Methods, 25(6):1207–1222.Google Scholar
Li, H., Chen, R., Nguyen, H., Chung, Y.-C., Gao, R., and Demirtas, H. (2020). RNGforGPD: Random Number Generation for Generalized Poisson Distribution. R package version 1.1.0.Google Scholar
Lindsey, J. K. and Mersch, G. (1992). Fitting and comparing probability distributions with log linear models. Computational Statistics and Data Analysis, 13(4):373–384.Google Scholar
Loeys, T., Moerkerke, B., De Smet, O., and Buysse, A. (2012). The analysis of zero- inflated count data: Beyond zero-inflated Poisson regression. British Journal of Mathematical and Statistical Psychology, 65(1):163–180.Google Scholar
Lord, D. (2006). Modeling motor vehicle crashes using Poisson-gamma models: Examining the effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter. Accident Analysis & Prevention, 38(4):751–766.Google Scholar
Lord, D., Geedipally, S. R., and Guikema, S. D. (2010). Extension of the application of Conway–Maxwell–Poisson models: Analyzing traffic crash data exhibiting underdispersion. Risk Analysis, 30(8):1268–1276.Google Scholar
Lord, D. and Guikema, S. D. (2012). The Conway–Maxwell–Poisson model for analyzing crash data. Applied Stochastic Models in Business and Industry, 28(2):122–127.Google Scholar
Lord, D., Guikema, S. D., and Geedipally, S. R. (2008). Application of the Conway– Maxwell–Poisson generalized linear model for analyzing motor vehicle crashes. Accident Analysis & Prevention, 40(3):1123–1134.Google Scholar
Lord, D. L. F. (2008). Effects of low sample mean values and small sample size on the estimation of the fixed dispersion parameter of Poisson- gamma models for modeling motor vehicle crashes: A Bayesian perspective. Safety Science, 46(5):751–770.Google Scholar
Lucas, J. M. (1985). Counted data CUSUM’s. Technometrics, 27(2):199–244.Google Scholar
Lucas, J. M. and Crosier, R. B. (1982). Fast initial response for CUSUM quality control schemes: Give your CUSUM a head start. Technometrics, 24(3):199–205.Google Scholar
Macaulay, T. B. (1923). Literary Essays Contributed to the Edinburgh Review. Oxford University Press.Google Scholar
MacDonald, I. L. and Bhamani, F. (2020). A time-series model for underdispersed or overdispersed counts. The American Statistician, 74(4):317–328.Google Scholar
Magnusson, A., Skaug, H., Nielsen, A., Berg, C., Kristensen, K., Maechler, M., van Bentham, K., Bolker, B., Sadat, N., Lüdecke, D., Lenth, R., O’Brien, J., and Brooks, M. (2020). glmmTMB: Generalized Linear Mixed Models using Template Model Builder, version 1.0.2.1. https://cran.r-project.org/web/packages/ glmmTMB/index.html.Google Scholar
Mamode Khan, N. and Jowaheer, V. (2010). A comparison of marginal and joint generalized quasi-likelihood estimating equations based on the COM–Poisson GLM: Application to car breakdowns data. International Journal of Mathematical and Computational Sciences, 4(1):23–26.Google Scholar
Mamode Khan, N., Jowaheer, V., Sunecher, Y., and Bourguignon, M. (2018). Modeling longitudinal INMA(1) with COM–Poisson innovation under non-stationarity: Application to medical data. Computational and Applied Mathematics, 37(12): 5217–5238.Google Scholar
Marschner, I. C. (2011). glm2: Fitting generalized linear models with convergence problems. R Journal, 3(2):12–15.Google Scholar
Marshall, A. W. and Olkin, I. (1985). A family of bivariate distributions generated by the bivariate Bernoulli distribution. Journal of the American Statistical Association, 80(390):332–338.Google Scholar
McCullagh, P. and Nelder, J. A. (1997). Generalized Linear Models, 2nd edition. Chapman & Hall/CRC Press.Google Scholar
Melo, M. and Alencar, A. (2020). Conway–Maxwell–Poisson autoregressive moving average model for equidispersed, underdispersed, and overdispersed count data. Journal of Time Series Analysis, 41(6):830–857.Google Scholar
Miaou, S.-P. and Lord, D. (2003). Modeling traffic crash-flow relationships for inter- sections: Dispersion parameter, functional form, and Bayes versus empirical Bayes. Transportation Research Record, 1840(1):31–40.Google Scholar
Mills, T. and Seneta, E. (1989). Goodness-of-fit for a branching process with immigration using sample partial autocorrelations. Stochastic Processes and their Applications, 33(1):151–161.Google Scholar
Minka, T. P., Shmueli, G., Kadane, J. B., Borle, S., and Boatwright, P. (2003). Computing with the COM–Poisson distribution. Technical Report 776, Dept. of Statistics, Carnegie Mellon University.Google Scholar
Mohammed, M. and Laney, D. (2006). Overdispersion in health care performance data: Laney’s approach. Quality and Safety in Health Care, 15(5):383– 384.Google Scholar
Molenberghs, G., Verbeke, G., and Demétrio, C. G. (2007). An extended random-effects approach to modeling repeated, overdispersed count data. Lifetime Data Analysis, 13(4):513–531.Google Scholar
Montgomery, D. C. (2001). Design and Analysis of Experiments. John Wiley & Sons, 5th edition.Google Scholar
Morris, D. S., Raim, A. M., and Sellers, K. F. (2020). A Conway–Maxwell-multinomial distribution for flexible modeling of clustered categorical data. Journal of Multivariate Analysis, 179:104651.Google Scholar
Morris, D. S. and Sellers, K. F. (2022). A flexible mixed model for clustered count data. Stats, 5(1):52–69.Google Scholar
Morris, D. S., Sellers, K. F., and Menger, A. (2017). Fitting a flexible model for longitudinal count data using the NLMIXED procedure. In SAS Global Forum Proceedings Paper 202-2017, pages 1–6, Cary, NC. SAS Institute. http://support.sas.com/resources/papers/proceedings17/0202-2017.pdf.Google Scholar
Nadarajah, S. (2009). Useful moment and CDF formulations for the COM–Poisson distribution. Statistics Papers, 50(3):617–622.Google Scholar
Nelsen, R. B. (2010). An Introduction to Copulas. Springer Publishing Company.Google Scholar
Ntzoufras, I., Katsis, A., and Karlis, D. (2005). Bayesian assessment of the distribution of insurance claim counts using reversible jump MCMC. North American Actuarial Journal, 9(3):90–108.Google Scholar
Oh, J., Washington, S., and Nam, D. (2006). Accident prediction model for railway- highway interfaces. Accident Analysis & Prevention, 38(2):346–356.Google Scholar
Olver, F. W. J. (1974). Asymptotics and Special Functions. Academic Press.Google Scholar
Ong, S. H., Gupta, R. C., Ma, T., and Sim, S. Z. (2021). Bivariate Conway–Maxwell– Poisson distributions with given marginals and correlation. Journal of Statistical Theory and Practice, 15(10):1–19.Google Scholar
Ord, J. K. (1967). Graphical methods for a class of discrete distributions. Journal of the Royal Statistical Society, Series A, 130(2):232–238.Google Scholar
Ord, J. K. and Whitmore, G. A. (1986). The Poisson-inverse Gaussian distribution as a model for species abundance. Communications in Statistics – Theory and Methods, 15(3):853–871.Google Scholar
Ötting, M., Langrock, R., and Maruotti, A. (2021). A copula-based multivariate hidden Markov model for modelling momentum in football. AStA Advances in Statistical Analysis.Google Scholar
Pal, S. and Balakrishnan, N. (2017). Likelihood inference for COM–Poisson cure rate model with interval-censored data and Weibull lifetimes. Statistical Methods in Medical Research, 26(5):2093–2113.Google Scholar
Pal, S., Majakwara, J., and Balakrishnan, N. (2018). An EM algorithm for the destructive COM–Poisson regression cure rate model. Metrika, 81(2):143–171.Google Scholar
Piegorsch, W. W. (1990). Maximum likelihood estimation for the negative binomial dispersion parameter. Biometrics, 46(3):863–867.Google Scholar
Pollock, J. (2014a). CompGLM: Conway–Maxwell–Poisson GLM and distribution functions, version 1.0. https://cran.r-project.org/web/packages/CompGLM/ index.html.Google Scholar
Pollock, J. (2014b). The CompGLM Package: Conway–Maxwell–Poisson GLM and distribution functions, 1.0 edition.Google Scholar
Puig, P., Valero, J., and Fernández-Fontelo, A. (2016). Some mechanisms leading to underdispersion.Google Scholar
R Core Team (2014). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.Google Scholar
Raim, A. M. and Morris, D. S. (2020). COMMultReg: Conway–Maxwell multinomial regression, version 0.1.0. https://cran.r-project.org/web/packages/commultreg/ index.html.Google Scholar
Rao, G. S., Aslam, M., Rasheed, U., and Jun, C.-H. (2020). Mixed EWMA–CUSUM chart for COM–Poisson distribution. Journal of Statistics and Management Systems, 23(3):511–527.Google Scholar
Reynolds, M. R. J. R. (2013). The Bernoulli CUSUM chart for detecting decreases in a proportion. Quality and Reliability Engineering International, 29(4):529–534.Google Scholar
RibeiroJr., E. E., Zeviani, W. M., Bonat, W. H., Demetrio, C. G., and Hinde, J. (2019). Reparametrization of COM–Poisson regression models with applications in the analysis of experimental data. Statistical Modelling. 20. 10.1177/1471082X19838651.Google Scholar
Ridout, M. S. and Besbeas, P. (2004). An empirical model for underdispersed count data. Statistical Modelling, 4(1):77–89.Google Scholar
Rigby, R. A. and Stasinopoulos, D. M. (2005). Generalized additive models for location, scale and shape (with discussion). Applied Statistics, 54:507–554.Google Scholar
Rodrigues, J., Cancho, V. G., de Castro, M., and Balakrishnan, N. (2012). A Bayesian destructive weighted Poisson cure rate model and an application to a cutaneous melanoma data. Statistical methods in medical research, 21(6):585–597.Google Scholar
Rodrigues, J., de Castro, M., Balakrishnan, N., and Cancho, V. G. (2011). Destructive weighted Poisson cure rate models. Lifetime Data Analysis, 17:333–346.Google Scholar
Rodrigues, J., de Castro, M., Cancho, V. G., and Balakrishnan, N. (2009). COM–Poisson cure rate survival models and an application to a cutaneous melanoma data. Journal of Statistical Planning and Inference, 139(10):3605–3611.Google Scholar
Rosen, O., Jiang, W., and Tanner, M. A. (2000). Mixtures of marginal models. Biometrika, 87(2):391–404.Google Scholar
Roy, S., Tripathi, R. C., and Balakrishnan, N. (2020). A Conway–Maxwell–Poisson type generalization of the negative hypergeometric distribution. Communications in Statistics – Theory and Methods, 49(10):2410–2428.Google Scholar
Rutherford, E., Geiger, H., and Bateman, H. (1910). The probability variations in the distribution of α particles. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 20(118):698–707.Google Scholar
Saez-Castillo, A. J., Conde-Sanchez, A., and Martinez, F. (2020). DGLMExtPois: Double Generalized Linear Models Extending Poisson Regression, version 0.1.3.Google Scholar
Saghir, A. and Lin, Z. (2014a). Control chart for monitoring multivariate COM–Poisson attributes. Journal of Applied Statistics, 41(1):200–214.Google Scholar
Saghir, A. and Lin, Z. (2014b). Cumulative sum charts for monitoring the COM– Poisson processes. Computers and Industrial Engineering, 68(1):65–77.Google Scholar
Saghir, A. and Lin, Z. (2014c). A flexible and generalized exponentially weighted moving average control chart for count data. Quality and Reliability Engineering International, 30(8):1427–1443.Google Scholar
Saghir, A., Lin, Z., Abbasi, S., and Ahmad, S. (2013). The use of probability limits of COM–Poisson charts and their applications. Quality and Reliability Engineering International, 29(5):759–770.Google Scholar
Santana, R. A., Conceição, K. S., Diniz, C. A. R., and Andrade, M. G. (2021). Type I multivariate zero-inflated COM–Poisson regression model. Biometrical Journal.Google Scholar
Sarmanov, O. V. (1966). Generalized normal correlation and two-dimensional Fréchet classes. Dokl. Akad. Nauk SSSR, 168(1):32–35.Google Scholar
SAS Institute. (2014). SAS/ETS(R) 13.1 User’s Guide. http://www.sas.com/.Google Scholar
Self, S. G. and Liang, K.-Y. (1987). Asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions. Journal of the American Statistical Association, 82(398):605–610.Google Scholar
Sellers, K. (2012a). A distribution describing differences in count data containing common dispersion levels. Advances and Applications in Statistical Sciences, 7(3):35–46.Google Scholar
Sellers, K. and Costa, L. (2014). CMPControl: Control Charts for Conway– Maxwell–Poisson Distribution, version 1.0. https://cran.r-project.org/web/packages/ CMPControl/index.html.Google Scholar
Sellers, K., Lotze, T., and Raim, A. (2019). COMPoissonReg: Conway–Maxwell– Poisson (COM–Poisson) Regression, version 0.7.0. https://cran.r-project.org/web/packages/COMPoissonReg/index.html.Google Scholar
Sellers, K., Morris, D. S., Balakrishnan, N., and Davenport, D. (2017a). multicmp: Flexible Modeling of Multivariate Count Data via the Multivariate Conway– Maxwell–Poisson Distribution, version 1.0. https://cran.r-project.org/web/packages/ multicmp/index.html.Google Scholar
Sellers, K. and Shmueli, G. (2009). A regression model for count data with observation-level dispersion. In Booth, J. G., editor, Proceedings of the 24th International Workshop on Statistical Modelling, pages 337–344, Ithaca, NY.Google Scholar
Sellers, K. and Shmueli, G. (2013). Data dispersion: Now you see it... now you don’t. Communications in Statistics – Theory and Methods, 42(17):1–14.Google Scholar
Sellers, K. F. (2012b). A generalized statistical control chart for over- or under-dispersed data. Quality and Reliability Engineering International, 28(1):59–65.Google Scholar
Sellers, K. F., Arab, A., Melville, S., and Cui, F. (2021a). A flexible univariate moving average time-series model for dispersed count data. Journal of Statistical Distributions and Applications, 8(1):1–12.Google Scholar
Sellers, K. F., Li, T., Wu, Y., and Balakrishnan, N. (2021b). A flexible multivariate distribution for correlated count data. Stats, 4(2):308–326.Google Scholar
Sellers, K. F. and Morris, D. S. (2017). Underdispersion models: Models that are “under the radar”. Communications in Statistics – Theory and Methods, 46(24):12075–12086.Google Scholar
Sellers, K. F., Morris, D. S., and Balakrishnan, N. (2016). Bivariate Conway–Maxwell– Poisson distribution: Formulation, properties, and inference. Journal of Multivariate Analysis, 150:152–168.Google Scholar
Sellers, K. F., Peng, S. J., and Arab, A. (2020). A flexible univariate autoregressive time-series model for dispersed count data. Journal of Time Series Analysis, 41(3): 436–453.Google Scholar
Sellers, K. F. and Raim, A. (2016). A flexible zero-inflated model to address data dispersion. Computational Statistics and Data Analysis, 99:68–80.Google Scholar
Sellers, K. F. and Shmueli, G. (2010). A flexible regression model for count data. Annals of Applied Statistics, 4(2):943–961.Google Scholar
Sellers, K. F., Shmueli, G., and Borle, S. (2011). The COM–Poisson model for count data: A survey of methods and applications. Applied Stochastic Models in Business and Industry, 28(2):104–116.Google Scholar
Sellers, K. F., Swift, A. W., and Weems, K. S. (2017b). A flexible distribution class for count data. Journal of Statistical Distributions and Applications, 4(22):1–21.Google Scholar
Sellers, K. F. and Young, D. S. (2019). Zero-inflated sum of Conway–Maxwell– Poissons (ZISCMP) regression. Journal of Statistical Computation and Simulation, 89(9):1649–1673.Google Scholar
Sheu, S.-H. and Chiu, W.-C. (2007). Poisson GWMA control chart. Communications in Statistics – Simulation and Computation, 36(5):1099–1114.Google Scholar
Shmueli, G., Minka, T. P., Kadane, J. B., Borle, S., and Boatwright, P. (2005). A useful distribution for fitting discrete data: Revival of the Conway–Maxwell–Poisson distribution. Applied Statistics, 54:127–142.Google Scholar
Şimşek, B. and Iyengar, S. (2016). Approximating the Conway–Maxwell–Poisson normalizing constant. Filomat, 30(4):953–960.Google Scholar
Skellam, J. G. (1946). The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of the Royal Statistical Society Series A, 109(3):296.Google Scholar
Spiegelhalter, D. (2005). Handling over-dispersion of performance indicators. Quality and Safety in Health Care, 14(5):347–351.Google Scholar
Stasinopoulos, D. M. and Rigby, R. A. (2007). Generalized additive models for location scale and shape (gamlss) in R. Journal of Statistical Software, 23(7):1–46.Google Scholar
Statisticat and LLC. (2021). LaplacesDemon: Complete Environment for Bayesian Inference. R package version 16.1.6.Google Scholar
Sunecher, Y., Khan, N. M., and Jowaheer, V. (2020). BINMA(1) model with COM– Poisson innovations: Estimation and application. Communications in Statistics – Simulation and Computation, 49(6):1631–1652.Google Scholar
Thall, P. F. and Vail, S. C. (1990). Some covariance models for longitudinal count data with overdispersion. Biometrics, 46(3):657–671.Google Scholar
Trivedi, P. and Zimmer, D. (2017). A note on identification of bivariate copulas for discrete count data. Econometrics, 5(1):1–11.Google Scholar
Waller, L. A., Carlin, B. P., Xia, H., and Gelfand, A. E. (1997). Hierarchical spatiotemporal mapping of disease rates. Journal of the American Statistical Association, 92(438):607–617.Google Scholar
Washburn, A. (1996). Katz distributions, with applications to minefield clearance. Technical Report ADA307317, Naval Postgraduate School Moterey CA Department of Operations Research.Google Scholar
Weems, K. S., Sellers, K. F., and Li, T. (2021). A flexible bivariate distribution for count data expressing data dispersion. Communications in Statistics – Theory and Methods.Google Scholar
Weiss, C. H. (2008). Thinning operations for modeling time series of counts—a survey. Advances in Statistical Analysis, 92(3):319–341.Google Scholar
Winkelmann, R. (1995). Duration dependence and dispersion in count-data models. Journal of Business & Economic Statistics, 13(4):467–474.Google Scholar
Winkelmann, R. and Zimmermann, K. F. (1995). Recent developments in count data modelling: Theory and application. Journal of Economic Surveys, 9(1):1–24.Google Scholar
Witowski, V. and Foraita, R. (2018). HMMpa: Analysing Accelerometer Data Using Hidden Markov Models. R package version 1.0.1.Google Scholar
Wood, S. N. (2012). On p-values for smooth components of an extended generalized additive model. Biometrika, 100(1):221–228.Google Scholar
Wu, G., Holan, S. H., Nilon, C. H., and Wikle, C. K. (2015). Bayesian binomial mixture models for estimating abundance in ecological monitoring studies. The Annals of Applied Statistics, 9(1):1–26.Google Scholar
Wu, G., Holan, S. H., and Wikle, C. K. (2013). Hierarchical Bayesian spatio-temporal Conway–Maxwell–Poisson models with dynamic dispersion. Journal of Agricultural, Biological, and Environmental Statistics, 18(3):335–356.Google Scholar
Yakovlev, A. Y. and Tsodikov, A. D. (1996). Stochastic Models of Tumor Latency and Their Biostatistical Applications. World Scientific.Google Scholar
Yee, T. W. (2008). The VGAM package. R News, 8(2):28–39.Google Scholar
Yee, T. W. (2010). The VGAM package for categorical data analysis. Journal of Statistical Software, 32(10):1–34.Google Scholar
Zeileis, A., Lumley, T., Graham, N., and Koell, S. (2021). sandwich: Robust Covariance Matrix Estimators, version 3.0-1. https://cran.r-project.org/web/packages/sandwich/sandwich.pdf.Google Scholar
Zhang, H. (2015). Characterizations and infinite divisibility of extended COM–Poisson distribution. International Journal of Statistical Distributions and Applications, 1(1):1–4.Google Scholar
Zhang, H., Tan, K., and Li, B. (2018). The COM-negative binomial distribution: modeling overdispersion and ultrahigh zero-inflated count data. Frontiers of Mathematics in China, 13:967–998.Google Scholar
Zhang, L., Govindaraju, K., Lai, C. D., and Bebbington, M. S. (2003). Poisson DEWMA control chart. Communications in Statistics – Simulation and Computation, 32(4):1265–1283.Google Scholar
Zhu, F. (2012). Modeling time series of counts with COM–Poisson INGARCH models. Mathematical and Computer Modelling, 56(9):191–203.Google Scholar
Zhu, L., Sellers, K., Morris, D., Shmueli, G., and Davenport, D. (2017a). cmpprocess: Flexible modeling of count processes, version 1.0. https://cran.rproject.org/web/packages/cmpprocess/index.html.Google Scholar
Zhu, L., Sellers, K. F., Morris, D. S., and Shmuéli, G. (2017b). Bridging the gap: A generalized stochastic process for count data. The American Statistician, 71(1): 71–80.Google Scholar
Zucchini, W., MacDonald, I. L., and Langrock, R. (2016). Hidden Markov Models for Time Series: An Introduction Using R. Chapman & Hall/CRC Press, 2nd edition.Google Scholar

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  • References
  • Kimberly F. Sellers, Georgetown University, Washington DC
  • Book: The Conway–Maxwell–Poisson Distribution
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