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Master's Dissertation
DOI
https://doi.org/10.11606/D.45.2018.tde-09042018-154057
Document
Author
Full name
Francimário Alves de Lima
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Paulo, 2018
Supervisor
Committee
Ferrari, Silvia Lopes de Paula (President)
Bayer, Fábio Mariano
Ospina, Patrícia Leone Espinheira
Title in Portuguese
Distribuições de probabilidade no intervalo unitário
Keywords in Portuguese
Banco Mundial
Distribuição beta
Distribuições contínuas no intervalo unitário
Abstract in Portuguese
A distribuição beta é a mais frequentemente utilizada para a modelagem de dados contínuos observados no intervalo unitário, como taxas e proporções. Embora seja flexível, admitindo formas variadas, tais como J, J invertido, U e unimodal, não é adequada em todas as situações práticas. Nesta dissertação fazemos uma revisão sobre distribuições contínuas no intervalo unitário englobando as distribuições beta, Kumaraswamy, simplex, gama unitária e beta retangular. Também abordamos uma ampla classe de distribuições obtida por transformações (Smithson e Merkle, 2013). Em particular, focamos em duas subclasses, uma apresentada e estudada por Lemonte e Bazán (2015), que chamaremos de classe de distribuições logito, e outra que chamaremos de classe de distribuições logito skew. Todas as distribuições consideradas são aplicadas a conjuntos de dados do Banco Mundial.
Title in English
Probability distributions in the unit interval
Keywords in English
Beta distribution
Continuous distributions in the unit interval
World Bank
Abstract in English
The beta distribution is the most frequently used for modeling continuous data observed in the unit interval, such as rates and proportions. Although flexible, assuming varied forms, such as J, inverted J, U and unimodal, it is not suitable in all practical situations. In this dissertation we make a review on continuous distributions in the unit interval encompassing the beta, Kumaraswamy, simplex, unit gamma and rectangular beta distributions. We also address a wide class of distributions obtained by transformations (Smithson and Merkle, 2013). In particular, we focus on two subclasses, one presented and studied by Lemonte and Bazán (2015), which we will call the logit class of distributions, and another that we will call the logit class of skew distributions. All distributions considered are applied to World Bank data sets.
 
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Publishing Date
2018-05-14
 
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