Quantile-Based Multivariate Log-Normal Distribution

We introduce a quantile-based multivariate log-normal distribution, providing a new multivariate skewed distribution with positive support. The parameters of this distribution are interpretable in terms of quantiles of marginal distributions and associations between pairs of variables, a desirable feature for statistical modeling purposes. We derive statistical properties of the quantile-based multivariate log-normal distribution involving the transformations, closed-form expressions for the mixed moments, expected value, covariance matrix, mode, Shannon entropy, and Kullback–Leibler divergence. We also present results on marginalization, conditioning, and independence. Additionally, we discuss parameter estimation and verify its performance through simulation studies. We evaluate the model fitting based on Mahalanobis-type distances. An application to children data is presented.

• Autores: Morán Vásquez, Raúl Alejandro; Roldán Correa, Alejandro; Nagar, Daya Krishna
• Tipo de recurso: Article of investigation
• Fecha de publicación: 2023
• Institución: Universidad de Antioquia
• Repositorio: Repositorio UdeA
• Idioma: eng
• OAI Identifier: oai:bibliotecadigital.udea.edu.co:10495/46090
• Acceso en línea: https://hdl.handle.net/10495/46090
• Palabra clave: Lognormal distribution; Independencia (matemáticas); Independence (Mathematics); Distribución (teoría de probabilidades); Distribution (probability theory); Método estadístico; Statistical methods; Análisis multivariante; Multivariate analysis; Kullback-Leiber divergence; Mixed moments; Quantile-based distribution; http://aims.fao.org/aos/agrovoc/c_7377; http://aims.fao.org/aos/agrovoc/c_28921; http://id.loc.gov/authorities/subjects/sh85078134
• Rights: openAccess
• License: http://creativecommons.org/licenses/by/4.0/