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Unusual-event processes for count data

  • Wanrudee Skulpakdee [1] ; Mongkol Hunkrajok
    1. [1] National Institute of Development Administration, Bangkok, Thailand
  • Localización: Sort: Statistics and Operations Research Transactions, ISSN 1696-2281, Vol. 46, Nº. 1, 2022, págs. 39-66
  • Idioma: inglés
  • Enlaces
  • Resumen
    • At least one unusual event appears in some count datasets. It will lead to a more concentrated (or dispersed) distribution than the Poisson, gamma, Weibull, Conway-Maxwell-Poisson (CMP), and Faddy (1997) models can accommodate. These well-known count models are based on the monotonic rates of interarrival times between successive events. Under the assumption of non-monotonic rates and independent exponential interarrival times, a new class of parametric models for unusual-event (UE) count data is proposed. These models are applied to two empirical applications, the number of births and the number of bids, and yield considerably better results to the above well-known count models.

  • Referencias bibliográficas
    • Ball, F. (1995). A note on variation in birth processes. The Mathematical Scientist 20, 50–55.
    • Bartlett, M. S. (1978). An Introduction to Stochastic Processes. Cambridge University Press, Cambridge, UK.
    • Cameron, A. C. and Johansson, P. (1997). Count data regression using series expansions: with applications. Journal of Applied Econometrics...
    • Chanialidis, C., Evers, L., Neocleous, T., and Nobile, A. (2018). Effcient Bayesian inference for COM-Poisson regression models. Statistics...
    • Conway, R. W. and Maxwell, W. L. (1962). A queuing model with state dependent service rates. Journal of Industrial Engineering 12, 132–136.
    • Cox, D. R. and Miller, H.D. (1965). The Theory of Stochastic Processes. Chapman and Hall, London, UK.
    • Crawford, F. W., Ho, L. S. T., and Suchard, M. A. (2018). Computational methods for birth-death processes. WIREs Computational Statistics...
    • Eddelbuettel, D., Francois, R., Allaire, J., Ushey, K., Kou, Q., Russell, N., Bates, D., and Chambers, J. (2021). Rcpp: Seamless R and C++...
    • Faddy, M. J. (1994). On variation in Poisson processes. The Mathematical Scientist 19, 47–51.
    • Faddy, M. J. (1997). Extended Poisson process modelling and analysis of count data. Biometrical Journal 39(4), 431–440.
    • Faddy, M. J. and Smith, D. M. (2008). Extended Poisson process modelling of dilution series data. Journal of the Royal Statistical Society....
    • Faddy, M. J. and Smith, D. M. (2011). Analysis of count data with covariate dependence in both mean and variance. Journal of Applied Statistics...
    • Fung, T., Alwan, A., Wishart, J., and Huang, A. (2019). mpcmp: Mean-parametrized Conway-Maxwell Poisson (COM-Poisson) regression. R package...
    • Goulet, V., Dutang, C., Maechler, M., Firth, D., Shapira, M., and Stadelmann, M. (2020). expm: Matrix exponential, log, ’etc’. R package version...
    • Jaggia, S. and Thosar, S. (1993). Multiple bids as a consequence of target management resistance: a count data approach. Review of Quantitative...
    • Jensen, A. (1953). Markoff chains as an aid in the study of Markoff processes. Scandinavian Actuarial Journal sup1, 87–91.
    • Kharrat, T. and Boshnakov, G. N. (2018). Countr: Flexible univariate count models based on renewal processes. R package version 3.5.2.
    • Kharrat, T., Boshnakov, G. N., McHale, I., and Baker, R. (2019). Flexible regression models for count data based on renewal processes. Journal...
    • McShane, B., Adrian, M., Bradlow, E. T., and Fader, P. S. (2008). Count models based on Weibull interarrival times. Journal of Business &...
    • Parthasarathy, P. R. and Sudhesh, R. (2006). Exact transient solution of a state-dependent birth-death process. Journal of Applied Mathematics...
    • Podlich, H. M., Faddy, M. J., and Smyth, G. K.(2004). Semi-parametric extended Poisson process models for count data. Statistics and Computing...
    • R Core Team (2019). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria.
    • Ross, S. M. (2010). Introduction to Probability Models, 10th Ed. Academic Press, San Diego, CA, USA.
    • Saez-Castillo, A. J. and Conde-Sanchez, A. (2013). A hyper-Poisson regression model for overdispersed and underdispersed count data. Journal...
    • Sellers, K. F., Lotze, T., and Raim, A. M. (2018). COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) regression. R package version 0.6.1.
    • Sellers, K. F. and Shmueli, G. (2010). A fexible regression model for count data. The Annals of Applied Statistics 4(2), 943–961.
    • Smith, D. M. and Faddy, M. J. (2016). Mean and variance modelling of underand overdispersed count data. Journal of Statistical Software 69(6),...
    • Smith, D. M. and Faddy, M. J. (2018). CountsEPPM: Mean and variance modeling of count data. R package version 3.0.
    • Winkelmann, R. (1995). Duration dependence and dispersion in count-data models. Journal of Business & Economic Statistics 13(4), 467–474.

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