Modeling electrical distribution networks with inhomogeneous Galton-Watson trees

In this paper we consider inhomogeneous Galton-Watson trees, and derive various moments for such processes: the number of vertices, the number of leaves, and the height of the tree. Also we make a simple condition of finiteness. We use these processes to model a data set consisting of electrical distribution networks, where we make a flexible framework for formulating models through the mean and variance of the offspring distributions. Furthermore, we introduce two mixture distributions as offspring distributions to reflect the particular form of the data. For estimation we use maximum likelihood estimation.