Normalized logistic wavelets: Applications to COVID-19 data in Italy

Abstract

In this paper we deal with the logistic wavelets introduced in \cite{RF}. We modify them by multiplying by appropriate coefficients so that their norm in the space $L^{2}(R)$ is equal to 1. We calculate the normalization coefficients using the Grosset-Veselov formula \cite{GV}, Eulerian numbers and Bernoulli numbers. Then we apply the logistic wavelets to model of the first wave of Covid-19 deaths in Italy in 2020. This example shows that even asymmetric and skewed data can be modeled, with high accuracy, by a sum of logistic functions.