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

TL;DR

This paper introduces normalized logistic wavelets, modifies them for unit norm, and applies them to accurately model the first wave of COVID-19 deaths in Italy, demonstrating their effectiveness on asymmetric data.

Contribution

It presents a normalization method for logistic wavelets and applies them to COVID-19 data modeling, showing high accuracy even with skewed data.

Findings

Normalized logistic wavelets have unit norm in L^2 space.

High-accuracy modeling of COVID-19 death data in Italy.

Effective for asymmetric and skewed data modeling.

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.