Thèse de Doctorat
DOI
https://doi.org/10.11606/T.104.2021.tde-03032022-141531
Document
Auteur
Nom complet
Yuri Antonio Iriarte Salinas
Unité de l'USP
Domain de Connaissance
Date de Soutenance
Editeur
São Carlos, 2021
Directeur
Jury
Andrade Filho, Mário de Castro (Président)
Cáceres, Fredy Walther Castellares
Labra, Filidor Edilfonso Vilca
Lima, Maria do Carmo Soares de
Rodrigues, Josemar
Titre en anglais
Lambert-F Univariate Distributions for Asymmetrical Data
Mots-clés en anglais
Baseline distribution
Distribution generator
Hazard rate function
Lambert W function
Maximum likelihood estimator
Probability density function
Shape parameter
Resumé en anglais
In this dissertation, we propose new univariate continuous distributions for modeling asymmetri- cal data. Initially, starting from a non-linear parametric transformation of an uniform random variable, we propose a new asymmetric one-parameter distribution that extends the uniform distribution, the so-called Lambert-uniform distribution. The transformation is expressed an- alytically in terms of the principal branch of the Lambert W function in such a way that the inverse transformation is expressed in terms of an exponential function. Consequently, the density function of the Lambert-uniform distribution has a simple closed form and exhibits increasing or decreasing monotonic behavior. Subsequently, based on the Lambert-uniform distribution, we propose a new distribution generator that allows adding one shape parameter to an arbitrary baseline distribution. The added parameter allows a variety of shapes for the density function of the resulting distribution, leading to an expansion of the skewness and kurtosis ranges of the baseline distribution. We observe that the parameter induced by the generator acts as a skewness parameter when the baseline distribution is symmetric. On the other hand, when the baseline distribution has positive support, we observe that the hazard rate function of the resulting distribution corresponds to a modification in the early times of the hazard rate function of the baseline distribution. This is exemplified through the study of four special cases obtained by considering the generalized-bimodal, slash, exponential and Rayleigh distributions as baseline distributions. We discuss the parameter estimation via the maximum likelihood method and evaluate the behavior of the estimators through simulation experiments. Finally, we consider some application examples that illustrate the usefulness of the proposed distributions in different real settings.
Titre en portugais
Mots-clés en portugais
Distribuição de referência
Função de taxa de risco
Função Lambert W