Advances and Applications in Statistics
Volume 52, Issue 4, Pages 215 - 234
(April 2018) http://dx.doi.org/10.17654/AS052040215 |
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JOINT MODELING OF CORRELATED TIME DURATIONS AND THEIR MARKS USING A WEIBULL‑POISSON MARKED POINT PROCESS MIXTURE MODELS
M. Y. Hassan
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Abstract: The focus of this paper is the joint modeling of interarrival times and the marks for marked point processes. Bivariate Mixture Transition (BMTD) models with the Weibull, Exponential and Rayleigh components will be used in modeling these marked point processes. BMTD models with Weibull and Rayleigh components are not yet considered in the literature of the mixture transition models. These models relax the key assumptions of the traditional models, including equally spaced interarrival times, duration dependence, count dependence, and the independence of the marks and the interarrival times. These assumptions have received considerable criticisms in the literature. Besides that, in modeling the interarrival times of the Poisson point processes and Poisson count models, the most commonly used probability distribution is the exponential. However, many researchers indicated that, Weibull and gamma distributions are more appropriate than the traditional exponential. Others like Winkelmann [31] pointed out the limitations of the gamma model, and instead left the right choice for the Weibull distribution. We propose a Weibull-Poisson BMTD (WPMTD) model for the joint modeling of the interarrival times and the associated marks of marked point process and compare the predictive performance with a Raleigh-Poisson BMTD (RPMTD) and the Exponential-Poisson BMTD (EPMTD) models. The Weibull-Poisson BMTD (WPMTD) model seems to capture the data better than the best competing Raleigh-Poisson BMTD (RPMTD) and the Exponential-Poisson BMTD (EPMTD) models. Prediction results obtained when these models are applied to two real datasets indicated that, WPMTD out performs other models in predicting interarrival times whereas the RPMTD dominated the prediction of the marks. |
Keywords and phrases: marked point processes, Erlang, Weibull-Poisson MTD, Raleigh-Poisson. |
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