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Doctoral Thesis
DOI
10.11606/T.45.2017.tde-06072017-102747
Document
Author
Full name
Yolanda Magaly Gómez Olmos
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2017
Supervisor
Committee
Bolfarine, Heleno (President)
Andrade Filho, Mário de Castro
Patriota, Alexandre Galvão
Rodrigues, Josemar
Valle, Reinaldo Boris Arellano
Title in Portuguese
Extensões de distribuições com aplicação à analise de sobrevivência
Keywords in Portuguese
Análise de sobrevivência
Fração de cura
Máxima verosissimilhança
Abstract in Portuguese
Nesta tese serão estudadas diferentes generalizações de algumas distribuições bem conhecidas na literatura para os tempos de vida, tais como exponencial, Lindley, Rayleigh e exponencial segmentada, entre outras, e compará-las com outras extensões com suporte positivo. A finalidade dessas generalizações é flexibilizar a função de risco de modo que possam assumir formas mais flexíveis. Além disso, pretende-se estudar propriedades importantes dos modelos propostos, tais como os momentos, coeficientes de curtose e assimetria e função quantílica, entre outras. A estimação dos parâmetros é abordada através dos métodos de máxima verossimilhança, via algoritmo EM (quando for possível) ou também, do método dos momentos. O comportamento desses estimadores foi avaliado em estudos de simulação. Foram ajustados a conjuntos de dados reais, usando uma abordagem clássica, e compará-los com outras extensões na literatura. Finalmente, um dos modelos propostos é considerado no contexto de fração de cura.
Title in English
Extensions of distributions with application to survival analysis
Keywords in English
Cure rate
Maximum likelihood
Survival analysis
Abstract in English
The main focus of this thesis is the study of generalizations for some positive distributions widely known in the literature of lifetime analysis, such as the exponential, Lindley, Rayleigh and segmented exponential. Comparisons of the proposed extensions and alternative extensions in the literature such as the generalized exponential distribution, are reported. Moreover, of interest is also the study of some properties of the proposed distributions such as moments, kurtosis and asymmetry coefficients, quantile functions and the risk function. Parameter estimation is approached via maximum likelihood (using the EM-algorithm when available) and the method of moments as initial parameter estimators. Results of simulation studies are reported comparing the performance of these estimators with small and moderate sample sizes. Further comparisons are reported for real data applications, where the proposed models show satisfactory performance. Finally, one of the models proposed is considered no context of cure rate.
 
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Publishing Date
2017-07-10
 
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