The cosine geometric distribution with count data modeling

Modeling and forecasting the COVID-19 pandemic with heterogeneous autoregression approaches: South Korea

“…For example, recently [51] proposed an integer-valued AR model with oscillating weighted cosine geometric innovations for modelling the COVID-19 series in some small island developing states. The weighted cosine geometric process accounts for oscillating patterns and, according to [52] , it outperforms well-known competing discrete models. The HAR model with the weighted cosine geometric innovation terms will be an interesting model to fit the COVID-19 series worldwide or in other countries with oscillation feature.…”

Insights on the trend of the Novel Coronavirus 2019 series in some Small Island Developing States: A Thinning-based Modelling Approach

“…These models may not be entirely convenient for the COVID-19 series, due to the extra oscillating patterns, as illustrated above. To account for these features, especially in the count data, Chesneau et al [14] proposed the Weighted Cosine Geometric model (WCG). The WCG model has been proven to mimic such patterns adequately in discrete data and to provide better fitting, as compared to other competing models.…”

“…The moment generating function is given by: This yields and is the support of and denotes the weight function. Chesneau et al [14] pointed out that and control the over-dispersion and periodicity. It is further shown in Chesneau et al [14] that WCG outperforms well-known competing discrete models: the Negative-Binomial, Geometric, Weighted Negative-Binomial Lindley [14] .…”

The Cos-Poisson model with a novel count regression analysis

“…In this paper, we introduce a new generalization of the Poisson distribution with the use of a cosine weight function defined by w(x) = w(x; β) = [cos(βx)] 2 , called the cosine Poisson (CosPois) distribution. We thus follow the spirit of the cosine geometric distribution introduced by Chesneau et al [7], but with the Poisson distribution as a baseline. The motivations behind this choice are as follows.…”