Multivariate Count-distance Base Copulas for Analysis of Spatial Point Pattern Data

Copula functions are powerful tools for construction the multivariate distribution of dependent continues variables in terms of their marginal distributions. Dependent count discrete data arise in the areas of spatial point pattern process. In this fields, it is necessary to find the correlation structure of counts variables and the distance to the special focus. These dependency is considered based on Poisson-Weibull distribution. In this paper, we extend the work by Omidi et al. (2016) to trivariate distribution by implementing the introducing of concentric buffers around to the special focus and pair copula to built a valid spatial point pattern copula. Next, for prediction of counts, trivariate distribution is achieved based on the continuous extension of counts random variables. Finally, based on achieved function we predict the number of Rats in terms of the number of Cockroaches and distance to focus in some important regions in Madrid city of Spain.

Copula functions are powerful tools for construction the multivariate distribution of dependent continues variables in terms of their marginal distributions. Dependent count discrete data arise in the areas of spatial point pattern process. In this fields, it is necessary to find the correlation structure of counts variables and the distance to the special focus. These dependency is considered based on Poisson-Weibull distribution. In this paper, we extend the work by Omidi et al. (2016) to trivariate distribution by implementing the introducing of concentric buffers around to the special focus and pair copula to built a valid spatial point pattern copula. Next, for prediction of counts, trivariate distribution is achieved based on the continuous extension of counts random variables. Finally, based on achieved function we predict the number of Rats in terms of the number of Cockroaches and distance to focus in some important regions in Madrid city of Spain.