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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

New trigonometric classes of probabilistic distributions

SOUZA, Luciano 13 November 2015 (has links)
Submitted by Mario BC (mario@bc.ufrpe.br) on 2016-08-01T12:46:49Z No. of bitstreams: 1 Luciano Souza.pdf: 1424173 bytes, checksum: 75d7ff2adb5077203e1371925327b71e (MD5) / Made available in DSpace on 2016-08-01T12:46:49Z (GMT). No. of bitstreams: 1 Luciano Souza.pdf: 1424173 bytes, checksum: 75d7ff2adb5077203e1371925327b71e (MD5) Previous issue date: 2015-11-13 / 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. / Nesta tese apresentamos e investigamos quatro novas classes trigonométricas de distribuições probabilísticas. As classes seno, cosseno, tangente e secante. Para cada uma das novas classes foi criada uma nova distribuição. Estas quatro novas distribuições foram usadas na modelagem de dados reais. Obtivemos uma simulação numérica, usando como base a distribuição exponencial, para se comparar os vicios (bias) e verificamos que, a medida que aumentamos o tamanho da amostra, o bias tende a zero. Alguns resultados numéricos para ver estimativas de máxima verossimilhança e os resultados para amostras finitas foram obtidos. Várias propriedades das classes e as suas distribuições foram obtidos. Obtemos as expansões, as estimativas de máxima verossimilhança, informações de Fisher, os quatro primeiros momentos, média, variância, assimetria e curtose, a função geradora de momentos e a entropia Rényi. Mostramos que todas as distribuições têm proporcionado bons ajustes quando aplicadas a dados reais, em comparação com outros modelos. Na comparação dos modelos foram utilizados: o Akaike Information Criterion (AIC), o Akaike Information Criterion Corrigido (CAIC), a informação Bayesian Criterion (BIC), o critério de informação Hannan Quinn (HQIC) e duas das principais estatísticas também foram utilizadas: Cramer -von Mises e Anderson-Darling. Por fim, apresentamos os resultados da análise e comparação dos resultados, e orientações para trabalhos futuros.

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