Abstract
The aim of this work is the statistical modelling of counts assuming low values and exhibiting sudden and large bursts that occur randomly in time. It is well known that bilinear processes capture these kind of phenomena. In this work the integer-valued bilinear INBL(1,0,1,1) model is discussed and some properties are reviewed. Classical and Bayesian methodologies are considered and compared through simulation studies, namely to obtain estimates of model parameters and to calculate point and interval predictions. Finally, an empirical application to real epidemiological count data is also presented to attest for its practical applicability in data analysis.
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- 1.
Steutel and van Harn operator “ϕ ∘” is defined by \(\phi \circ X=\sum _{i=1}^{X}Y_i\) where {Y i}, i = 1, …, X, is a sequence of independent and identically distributed (i.i.d.) counting random variables with mean ϕ and X is a non-negative integer-valued random variable, independent of Y . If Y i is a Bernoulli random variable, we have the binomial thinning operator.
- 2.
The computation of Bayesian estimates is very demanding in terms of CPU time. Using an Inter Core i5 @ 1.8 GHz-4 GB RAM, the average computation time for producing the estimates of the parameters for samples with size n = 100 is approximately 3 days.
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Acknowledgements
This work was supported by Portuguese funds through the CIDMA—Center for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology (“FCT—Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013.
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Pereira, I., Silva, N. (2018). Statistical Modelling of Counts with a Simple Integer-Valued Bilinear Process. In: Oliveira, T., Kitsos, C., Oliveira, A., Grilo, L. (eds) Recent Studies on Risk Analysis and Statistical Modeling. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-76605-8_25
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