Unit-log-symmetric models: Characterization, statistical properties and its use in analyzing internet access data

TL;DR

This paper introduces a flexible family of unit-log-symmetric models for data in (0,1), explores their mathematical properties, and demonstrates their application to internet access data analysis.

Contribution

It characterizes the unit-log-symmetric family, detailing properties and special cases, and applies these models to real-world internet access data.

Findings

The models effectively fit internet access data.

Mathematical properties are thoroughly derived.

Practical illustrations demonstrate usability.

Abstract

We present here a unit-log-symmetric model based on the bivariate log-symmetric distribution. It is a flexible family of distributions over the interval $(0, 1)$. We then discuss its mathematical properties such as stochastic representation, symmetry, modality, moments, quantile function, entropy and maximum likelihood estimators, paying particular attention to the special cases of unit log-normal, unit-log-Student-$t$ and unit-log-Laplace distributions. Finally, some empirical results and practical illustrations are presented.