# On the Mean Residual Life of Cantor-Type Distributions: Properties and Economic Applications

## TL;DR

This paper analyzes the mean residual life function of Cantor-type distributions, revealing their properties and demonstrating their practical applicability in economic modeling of markets with bandwagon effects.

## Contribution

It provides a detailed study of the MRL function for Cantor distributions and extends these properties to a parametric family, showing their relevance for economic applications.

## Key findings

- MRL function is continuous everywhere
- MRL is locally decreasing outside the Cantor set
- Cantor-type distributions can model markets with bandwagon effects

## Abstract

In this paper, we consider the mean residual life (MRL) function of the Cantor distribution and study its properties. We show that the MRL function is continuous at all points, locally decreasing at all points outside the Cantor set and has a unique fixed point which we explicitly determine. These properties readily extend to the parametric family of p-singular, Cantor type distributions introduced by Mandelbrot (1983). The findings offer evidence that, contrary to common perceptions, Cantor-type distributions are tractable enough to be considered for practical applications. We provide such an example from the field of economics in which Cantor-type distributions can be used to model markets with recurrent bandwagon effects and show that earlier anticipated bandwagon effects lead to higher monopolistic prices. We conclude with a simple implementation of the algorithm by Chalice (1991) to plot Cantor-type distributions.