New trigonometric classes of probabilistic distributions

• Ano de defesa: 2015
• Autor(a) principal: SOUZA, Luciano
• Orientador(a): OLIVEIRA JUNIOR, Wilson Rosa de
• Banca de defesa: RAMOS, Manoel Wallace Alves, SILVA, Frank Sinatra Gomes da, SILVA, Ronaldo Venâncio da
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal Rural de Pernambuco
• Programa de Pós-Graduação: Programa de Pós-Graduação em Biometria e Estatística Aplicada
• Departamento: Departamento de Estatística e Informática
• País: Brasil
• Palavras-chave em Português: Classe trigonométrica; Distribuição probabilística; Função univariada
• Palavras-chave em Inglês: Trigonometric classes; Probability distributions; Univariate functions
• Área do conhecimento CNPq: CIENCIAS EXATAS E DA TERRA::PROBABILIDADE E ESTATISTICA
• Link de acesso: http://www.tede2.ufrpe.br:8080/tede2/handle/tede2/5127

In this thesis, four new probabilistic distribution classes are presented and investigated: sine, cosine, tangent and secant. For each of which a new kind of distribution was created, which were used for modelling real life data.By having an exponential distribution to compare the biases, a numerical simulation was obtained, making it possible to verify that the bias tends to zero as the sample size is increased. In addition to that, some numerical results for checking maximum likelihood estimates, as well as the results for finite samples, were obtained, just as much as several class properties and their respective distributions were also obtained, along with the expansions, maximum likelihood estimates, Fisher information, the first four moments, average, variance, skewness, and kurtosis, the generating function of moments and Renyi’s entropy. It was evidenced that all distributions have shown good fit when applied to real life data, when in comparison to other models. In order to compare the models, the Akaike Information Criterion (AIC), the Corrected Akaike Information Criterion (CAIC), the Bayesian Information Criterion (BIC), the Hannan Quinn Information Criterion (HQIC) were used, along with two other main statistic sources: Cramer-Von Mises and Anderson-Darling. As a final step, the results of the analyses and the comparison of the results are brought up, as well as a few directions for future works.