Extensions of the normal distribution using the odd log-logistic family: theory and applications

• Ano de defesa: 2017
• Autor(a) principal: Braga, Altemir da Silva
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Biblioteca Digitais de Teses e Dissertações da USP
• Palavras-chave em Português: Estatística experimental; Experimental designs; Extensions of the normal distribution; Família de distribuição; Families distributions; Generating function; Likelihood; Log-logística; Modelo de Regressão; Quantile function; Quartiles residuals; Regression model; Simulation studies
• Link de acesso: http://www.teses.usp.br/teses/disponiveis/11/11134/tde-02102017-092313/

In this study we propose three new distributions and a study with longitudinal data. The first was the Odd log-logistic normal distribution: theory and applications in analysis of experiments, the second was Odd log-logistic t Student: theory and applications, the third was the Odd log-logistic skew normal: the new distribution skew-bimodal with applications in analysis of experiments and the fourth regression model with random effect of the Odd log-logistic skew normal distribution: an application in longitudinal data. Some have been demonstrated such as symmetry, quantile function, some expansions, ordinary incomplete moments, mean deviation and the moment generating function. The estimation of the model parameters were approached by the method of maximum likelihood. In applications were used regression models to data from a completely randomized design (CRD) or designs completely randomized in blocks (DBC). Thus, the models can be used in practical situations for as a completely randomized designs or completely randomized blocks designs, mainly, with evidence of asymmetry, kurtosis and bimodality.