Some new families of continuos distributions
The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean t...
| Main Author: | MARINHO, Pedro Rafael Diniz |
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| Other Authors: | CORDEIRO, Gauss Moutinho |
| Format: | doctoralThesis |
| Language: | por |
| Published: |
Universidade Federal de Pernambuco
2017
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| Subjects: | |
| Online Access: |
https://repositorio.ufpe.br/handle/123456789/18862 |
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| Summary: |
The area of survival analysis is important in Statistics and it is commonly applied in biological sciences, engineering, social sciences, among others. Typically, the time of life or failure can have different interpretations depending on the area of application. For example, the lifetime may mean the life itself of a person, the operating time of equipment until its failure, the time of survival of a patient with a severe disease from the diagnosis, the duration of a social event as a marriage, among other meanings. The time of life or survival time is a positive continuous random variable, which can have constant, monotonic increasing, monotonic decreasing or non-monotonic (for example, in the form of a U) hazard function. In the last decades, several families of probabilistic models have been proposed. These models can be constructed based on some transformation of a parent distribution, commonly already known in the literature. A given linear combination or mixture of G models usually defines a class of probabilistic models having G as a special case. This thesis is composed of independent chapters. The first and last chapters are short chapters that include the introduction and conclusions of the study developed. Two families of distributions, namely the exponentiated logarithmic generated (ELG) class and the geometric Nadarajah-Haghighi (NHG) class are studied. The last one is a composition of the Nadarajah-Haghighi and geometric distributions. Further, we develop a statistical library for the R programming language called the AdequacyModel. This is an improvement of the package that was available on CRAN (Comprehensive R Archive Network) and it is currently in version 2.0.0. The two main functions of the library are the goodness.fit and pso functions. The first function allows to obtain the maximum likelihood estimates (MLEs) of the model parameters and some goodness-of-fit of the fitted probabilistic models. It is possible to choose the method of optimization for maximizing the log-likelihood function. The second function presents the method meta-heuristics global search known as particle swarm optimization (PSO) proposed by Eberhart and Kennedy (1995). Such methodology can be used for obtaining the MLEs necessary for the calculation of some measures of adequacy of the probabilistic models. |
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