Modeling electrical distribution networks with inhomogeneous Galton-Watson trees

TL;DR

This paper models electrical distribution networks using inhomogeneous Galton-Watson trees, deriving moments and introducing mixture distributions for flexible data representation, with maximum likelihood estimation for parameter fitting.

Contribution

It introduces a novel framework for modeling electrical networks with inhomogeneous Galton-Watson trees, including mixture offspring distributions and moment calculations.

Findings

Derived moments for inhomogeneous Galton-Watson trees.

Proposed mixture distributions for offspring modeling.

Applied maximum likelihood estimation for parameter inference.

Abstract

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.