Hierarchical logistic equation to describe the dynamical behavior of penetration rates

TL;DR

This paper introduces a hierarchical logistic equation model that incorporates memory effects to better describe the dynamics of penetration rates, demonstrated through improved fit to iPod sales data.

Contribution

The paper presents a novel hierarchical logistic model with memory, enhancing the traditional logistic equation for more accurate representation of penetration dynamics.

Findings

Model fits iPod sales data better than standard logistic model

Incorporating memory improves the accuracy of penetration rate modeling

Hierarchical logistic equation captures complex dynamical behavior

Abstract

We propose a hierarchical logistic equation as a model to describe the dynamical behavior of a penetration rate of a prevalent stuff. In this model, a memory, how many people who already possess it a person who does not process it yet met, is considered, which does not exist in the logistic model. As an application, we apply this model to iPod sales data, and find that this model can approximate the data much better than the logistic equation.