Larceny trend in some areas of Mauritius via a bivariate INAR(1) model with dispersed COM-Poisson innovations

References

• Best, K. 2001. “Probability Distributions of Language Entities.” Journal of Quantitative Linguistics 8:1–11. doi: 10.1076/jqul.8.1.1.4091.
   Google Scholar
• Boatwright, P., S. Borle, and J. Kadane. 2003. “A Model of the Joint Distribution of Purchase Quantity and Timing.” Journal of the American Statistical Association 98:564–72. doi: 10.1198/016214503000000404.
   Web of Science ®Google Scholar
• Borle, S., P. Boatwright, and J. Kadane. 2006. “The Timing of Bid Placement and Extent of Multiple Bidding: An Empirical Investigation Using Ebay Online Auctions.” Statistical Science 21:194–205. doi: 10.1214/088342306000000123.
   Web of Science ®Google Scholar
• Borle, S., U. Dholakia, S. Singh, and R. Westbrook. 2007. “The Impact of Survey Participation on Subsequent Behavior: An Empirical Investigation.” Marketing Science 26: 711–26. doi: 10.1287/mksc.1070.0268.
   Web of Science ®Google Scholar
• Cui, Y., and Zhu, F. 2018. “A New Bivariate Integer-Valued GARCH Model Allowing for Negative Cross-Correlation.” Test 27:428–52. doi: 10.1007/s11749-017-0552-4.
   Web of Science ®Google Scholar
• Duhart, D. 2000. “Urban, Suburban, and Rural Victimization.” Urban, Suburban, and Rural Victimization 1:1–12.
   Google Scholar
• Esteves, A. 1999. “A criminalidade na cidade de lisboa.” Uma Geografia da Insegurança, Edições Colibri, Lisboa.
   Google Scholar
• Freeland, R., and B. McCabe. 2004a. “Analysis of Low Count Time Series Data by Poisson Autoregression.” Journal of Time Series Analysis 25(5):701–22. doi: 10.1111/j.1467-9892.2004.01885.x.
   Web of Science ®Google Scholar
• Freeland, R., and B. McCabe. 2004b. “Forecasting Discrete Valued Low Count Time Series.” International Journal of Forecasting 20:427–34. doi: 10.1016/S0169-2070(03)00014-1.
   Web of Science ®Google Scholar
• Glaeser, E., and B. Sacerdote. 1999. “Why is There More Crime in Cities?” Journal of Political Economy, 107(6):225–58.
   Web of Science ®Google Scholar
• Jowaheer, V., N. Mamode Khan, and Y. Sunecher. 2017b. “A BINAR(1) Time Series Model with Cross-Correlated COM-Poisson Innovations.” Communication in Statistics—Theory and Methods 47(5):1133–54. doi: 10.1080/03610926.2017.1316400.
   Web of Science ®Google Scholar
• Kalyanam, K., S. Borle, and P. Boatwright. 2007. “Deconstructing Each Item’s Category Contribution.” Maketing Science 26:327–41. doi: 10.1287/mksc.1070.0270.
   Web of Science ®Google Scholar
• Lord, D., S. Geedipally, and S. Guikema. 2010. “Extension of the Application of Conway–Maxwell Poisson Models: Analysing Traffic Crash Data Exhibiting Underdispersion.” Risk Analysis 30:1268–76. doi: 10.1111/j.1539-6924.2010.01417.x.
   PubMed Web of Science ®Google Scholar
• Lord, D., S. Guikema, and S. Geedipally. 2008. “Application of Conway-Maxwell Poisson for Analyzing Motor Vehicle Crashes.” Accident Analysis and Prevention 40:1123–34. doi: 10.1016/j.aap.2007.12.003.
   PubMed Web of Science ®Google Scholar
• Mamode Khan, N., W. Rumjaun, Y. Sunecher, and V. Jowaheer. 2017. “Computing with Bivariate COM-Poisson Model Under Different Copulas.” Journal of Monte Carlo Methods and Applications 23(2):1–16.
   Web of Science ®Google Scholar
• Mamodekhan, N., and V. Jowaheer. 2013. “Comparing Joint GQL Estimation and GMM Adaptive Estimation in COM-Poisson Longitudinal Regression Model.” Communication Statistics—Simulation C 42(4):755–70. doi: 10.1080/03610918.2012.655831.
   Web of Science ®Google Scholar
• Mamodekhan, N., Y. Sunecher, and V. Jowaheer. 2016b. “Modelling a Non-Stationary BINAR(1) Poisson Process.” Journal of Statistical Computation and Simulation 86:3106–26. doi: 10.1080/00949655.2016.1150482.
   Web of Science ®Google Scholar
• Mawby, R. 2007. “Crime, Place and Explaining Rural Hotspots.” International Journal of Rural Crime 1:21–43.
   Google Scholar
• McCullagh, P., and J. Nelder. 1999. Generalized Linear Models. 2nd ed., New York: Chapman and Hall, 26.
   Google Scholar
• McKenzie, E. 1985. “Some Simple Models for Discrete Variate Time Series.” Water Resources Bulletin 21(4): 645–50. doi: 10.1111/j.1752-1688.1985.tb05379.x.
   Google Scholar
• Rennison, C. 2003. Criminal Victimization 2002. Washington, DC: U.S. Department of Justice.
   Google Scholar
• Sampson, R., and J. Wooldredge. 1987. “Linking the Micro-and Macro-Level Dimensions of Lifestyle-Routine Activity and Opportunity Models of Predatory Victimization.” Journal of Quantitative Criminology 3(4):371–93. doi: 10.1007/BF01066837.
   Google Scholar
• Santana, P., R. Santos, C. Costa, N. Roque, and A. Loureiro. 2009. “Crime and Urban Environment: Impact on Human Health. City Futures in a Globalising World.” An international conference on globalism and urban change, 4–6 June 2009, Madrid.
   Google Scholar
• Sellers, K., D. Morris, and N. Balakrishnan. 2016. “Bivariate Conway–Maxwell–Poisson Distribution: Formulation, Properties and Inference.” Journal of Multivaiate Analysis 150:152–68. doi: 10.1016/j.jmva.2016.04.007.
   Web of Science ®Google Scholar
• Sellers, K., S. Borle and G. Shmueli. 2012. “The COM–Poisson Model for Count Data: A Survey of Methods and Applications.” Applied Stochastic Models in Business and Industry, 22:104–16. doi: 10.1002/asmb.918.
   Web of Science ®Google Scholar
• Shmueli, G., T. Minka, J. Borle, and P. Boatwright. 2005. “A Useful Distribution for Fitting Discrete Data.” Applied Statistics, Journal of Royal Statistical Society C 54(1):127–42. doi: 10.1111/j.1467-9876.2005.00474.x.
   Web of Science ®Google Scholar
• Siegel, J. 2010. Criminology: The Core. New York: Cengage.
   Google Scholar
• Singh, S., S. Borle, and D. Jain. 2009. “A Generalized Framework for Estimating Customer Lifetime Value When Customer Lifetimes Are Not Observed.” Quantitative Marketing and Economics 7:181–205. doi: 10.1007/s11129-009-9065-0.
   Web of Science ®Google Scholar
• Steutel, F., and Van Harn, K. 1979. “Discrete Analogues of Self-Decomposability and Stability.” The Annals of Probability 7:3893–899. doi: 10.1214/aop/1176994950.
   Web of Science ®Google Scholar
• Sunecher, Y., N. Mamodekhan, and V. Jowaheer. 2017. “A gql estimation approach for analysing non-stationary over-dispersed BINAR(1) time series.” Journal of Statistical Computation and Simulation 87(10):1911–24. doi: 10.1080/00949655.2017.1296152.
   Web of Science ®Google Scholar
• Wedderburn, R. 1974. “Quasi-Likelihood Functions, Generalized Linear Models, and the Gauss–Newton Method.” Biometrika 61(3):439–47. doi: 10.1093/biomet/61.3.439.
   Web of Science ®Google Scholar
• Wimmer, G., R. Kohler, R. Grotjahn, and G. Altmann. 1994. “Toward a Theory of Word Length Distribution.” Journal of Quantitative Linguistics 1:98–106. doi: 10.1080/09296179408590003.
   Google Scholar
• Zhu, F. 2012. “Modelling Time Series of Counts with COM–Poisson INGARCH Models.” Mathematical and Computer Modelling 56:191–203. doi: 10.1016/j.mcm.2011.11.069.
   Google Scholar