Essays on new models and the Mellin transform: experiments in survival and radar data

• Ano de defesa: 2018
• Autor(a) principal: VASCONCELOS, Josimar Mendes de
• Orientador(a): NASCIMENTO, Abraão David Costa do
• Tipo de documento: Tese
• Tipo de acesso: Acesso aberto
• Idioma: eng
• Instituição de defesa: Universidade Federal de Pernambuco
• Programa de Pós-Graduação: Programa de Pos Graduacao em Estatistica
• País: Brasil
• Palavras-chave em Português: Estatística; Análise de sobrevivência
• Link de acesso: https://repositorio.ufpe.br/handle/123456789/29754

Survival data have been applied in several contexts, such as survival time of mechanical components, the failure times of electrical insulator films, and in censored data from head-and-neckcancer clinical trials. The resulting data are positive-valued and are often censored of heavy tails. This latter fact suggests that tailored tools are necessary for modelling survival data behavior. In particular, there is a need for flexible models; inferential methods, such as estimation and goodness-of-fit (GoF); and conditional representation (e.g., regression and time series models). Several models have been proposed to describe survival data based on distribution families derived from transformations of reference distributions (called baselines). One of the most important derived distribution families is the beta-G family introduced by Eugene et al. [Beta-normal distribution and its applications. Communication in Statistics-Theory and Methods, 31, 497-512]. Although the beta-G class is capable of producing even distributions for bimodal data, it requires both efficient estimation methods and GoF criteria. GoF methodology proposals are sought because not rarely it is hard to distinguish models within the beta-G class using: (i) criteria without a cut-off point rule or (ii) criteria originally suitable for nested models (e.g., the Akaike Information Criteria). Further, the likelihood function for beta-G models in real and synthetic experiments have suggested the proposal of estimation criteria which do not involve such function. In this thesis, the synthetic aperture radar (SAR) imagery is taken as a concrete context for data modelling. SAR is widely regarded as an important tool for remote sensing, partly because of its ability to operate independently of atmospheric conditions and producing images in high spatial resolution. However, features from SAR images are corrupted by a multiplicative noise that imposes the use of specifically designed probabilistic models. An important SAR feature is the SAR intensity image, which is defined as the norm of a complex return. Further, experiments with real SAR intensities often produce multimodal data. Several works aimed at modeling SAR intensity data by means of distribution mixtures, but such strategy may impose a large number of parameters. In this thesis, we adopt the Mellin transform as a way to derive new tools for the understanding of survival analysis data. With this we propose: (i) new qualitative and quantitative GoF measures suitable for survival analysis data and (ii) a unique estimation method not based on the likelihood function. In the context of SAR imagery analysis, we introduce: (i) two new probabilistic models: the compound Poisson-truncated Cauchy and the G-G family with three and four parameters, respectively; and (ii) a regression model at the Gɪ⁰ distribution for speckled data.