Banca de DEFESA: JOÃO SILVA ROCHA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : JOÃO SILVA ROCHA
DATE: 30/08/2023
TIME: 13:30
LOCAL: meet.google.com/pjr-nkkb-hnr
TITLE:

Constructor methods of probabilistic distribution classes via function compositions

KEY WORDS:

baseline; biometrics; applied statistics; probability.

PAGES: 246
BIG AREA: Ciências Agrárias
AREA: Agronomia
SUMMARY:

The study of the constructors of probabilistic distribution classes by composition of functions aims to present six methods that generalize and generate probability distributions from the composition of functions. The methods proposed here allow the construction of classes of distributions, using monotonic functions of predefined distributions. With these methods it is possible to find new probabilistic distributions, classes of probabilistic distributions and also families of probability distributions, including some already present in the literature. Propositions are presented for the construction of the methods of this work, after that, tables are displayed with some values and pairs of increasing and decreasing continuous functions, together with their derivatives to feed the expressions of the constructor methods, generating some subcases of these methods. Initially, it is presented in this study, the methods that generate classes of probabilistic distributions, via compositions of cumulative distribution functions – cdf, in which baseline mixtures will be used from the construction of connection functions, together with the distribution construction methods. Next, methods for generating classes of probabilistic distributions by probability density function composition – pdf, based on the construction of linkage functions with baseline mixtures are presented. Studies of the supports of the functional generators of probabilistic distributions and the identifiability of the classes generated by the proposed methods are also developed. Some applications of these methods on simulated or real data are explained. In addition, for the classes and distributions generated by the functional models of the cdf and the pdf, there is the development of the expansions of the cdf and the pdf, the risk function, expansions for moments of order m, and for the moment generating function, as well as for the characteristic function, the expansions of central moments m and for the general coefficient, for the mean deviation and quantile deviation, the derivatives of the log-likelihood function and, the entropies of Shannon and Renyi. As a result, applications of a case of the methods are developed in which they are used in simulated data and/or in real data, thus pointing out the viability and generalization that serve as an anchorage for other researches in the different branches of the agricultural sciences.

COMMITTEE MEMBERS:
Externo à Instituição - CICERO CARLOS RAMOS DE BRITO - IFPE
Externo à Instituição - JOSE ARAUJO DOS SANTOS JUNIOR - UFPE
Interno - KLEBER NAPOLEAO NUNES DE OLIVEIRA BARROS
Presidente - MOACYR CUNHA FILHO
Interno - WILSON ROSA DE OLIVEIRA JUNIOR