Weighted Cook-Johnson Copula and their Characterizations: Application to Probably Modeling of the Hot Spring Eruptions

Copulas have emerged as a practical method for multivariate modeling. A limited amount of work has been conducted regarding the application of copula-based modeling in context analysis. This study generalizes the Cook-Johnson copula under the appropriate weighted function and provides examples and the properties of the generalized Cook-Johnson copula. Results show that the generalized Cook-Johnson copula is suitable for probable modeling of hot spring eruption

A New Family Of Time Series To Model The Decreasing Relative Increment Of Spreading Of An Outbreak

Introduction: There are different mathematical models describing the propagation of an epidemic. These models can be divided into phenomenological, compartmental, deep learning, and individual-based methods. From other viewpoints, we can classify them into macroscopic or microscopic, stochastic or deterministic, homogeneous or heterogeneous, univariate or multivariate, parsimonious or complex, or forecasting or mechanistic. This paper defines a novel univariate bi-partite time series model able to describe spreading a communicable infection in a population in terms of the relative increment of the cumulative number of confirmed cases. The introduced model can describe different stages of the first wave of the outbreak of a communicable disease from the start to the end. Methods: The outcome of the model is relative increment, and it has five positive parameters: the length of the first days of spreading and the relative increment in these days, the potent of the mildly decreasing trend (after the significant decrease), and the adjusting coefficient to adapt this trend to the initial pattern, and the fixed ratio of the mean to the variance. Results: We use it to describe the propagation of various disease outbreaks, including the SARS (2003), the MERS (2018), the Ebola (2014-2016), the HIV/AIDS (1990-2018), the Cholera (2008-2009), and the COVID-19 epidemic in Iran, Italy, the UK, the USA, China and four of its provinces; Beijing, Guangdong, Shanghai, and Hubei (2020). In all mentioned cases, the model has an acceptable performance. In addition, we compare the goodness of this model with the ARIMA models by fitting the propagation of COVID-19 in Iran, Italy, the UK, and the USA. Conclusion: The introduced model is flexible enough to describe a broad range of epidemics. In comparison with ARIMA time series models, our model is more initiative and less complicated, it has fewer parameters, the estimation of its parameters is more straightforward, and its forecasts are narrower and more accurate. Due to its simplicity and accuracy, this model is a good tool for epidemiologists and biostatisticians to model the first wave of an epidemic

Weighted Clayton Copulas and their Characterizations: Application to Probable Modeling of the Hydrology Data

Abstract: Copulas have recently emerged as practical methods for multivariate modeling. To our knowledge, only a limited amount of work has been done to apply copula-based modeling in context analysis. In this study, we generalized Clayton copula under the appropriate weighted function. In some examples, bivariate distributions by using the weighted Clayton copula are generalized. Also the properties of generalized Clayton copula are provided. The Clayton copula and weighted Clayton model cannot be used for negative dependence. These have been used to study left tail dependence. This property is stronger in weighted Clayton model with respect to ordinary Clayton copula. It will also be shown that the generalized Clayton copula is suitable for the probable modeling of the hydrology data