Facultad de Ciencias Básicas

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http://repositorioabierto.uantof.cl/handle/uantof/1

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Examinando Facultad de Ciencias Básicas por Autor "Arrué, Jaime"

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  • Miniatura
    Ítem
    A Bimodal Extension of the Beta-Binomial Distributionwith Applications
    (MDPI, 2024) Reyes, Jimmy; Najera Zuloaga, Josu; Lee, Dae-Jin; Arrué, Jaime; Iriarte, Yuri A.
    In this paper, we propose an alternative distribution to model count data exhibitinguni/bimodality. It arises as a weighted version of the beta-binomial distribution, which is defined bya parametric weight function that admits up to two modes for the resulting probability mass function.Like the baseline beta-binomial distribution, the proposed distribution performs well in modelingoverdispersed binomial data. Structural properties of the new distribution are studied. Raw momentsare derived, which are used to describe the dispersion behavior relative to the mean and the skewnessbehavior. Parameter estimation is carried out using the maximum likelihood method. A simulationstudy is conducted in order to illustrate the behavior of the estimators. Finally, two applicationsillustrating the usefulness of the proposal are presented.
  • Miniatura
    Ítem
    A New Multimodal Modification of the Skew Family of Distributions: Properties and Applications to Medical and Environmental Data
    (MDPI, 2024) Reyes, Jimmy; Rojas, Mario A.; Cortés, Pedro L.; Arrué, Jaime
    The skew distribution has the characteristic of appropriately modeling asymmetric unimodal data. However, in practice, there are several cases in which the data present more than one mode. In the literature, it is possible to find a large number of authors who have studied extensions based on the skew distribution to model this type of data. In this article, a new family is introduced,consisting of a multimodal modification to the family of skew distributions. Using the methodology of the weighted version of a function, we perform the product of the density function of a family of skew distributions with a polynomial of degree 4, thus obtaining a more flexible model that allows modeling data sets, whose distribution contains at most three modes. The density function, some properties, moments, skewness coefficients, and kurtosis of this new family are presented. This study focuses on the particular cases of skew-normal and Laplace distributions, although it can be applied to any other distribution. A simulation study was carried out, to study the behavior of the model parameter estimates. Illustrations with real data, referring to medicine and environmental data, show the practical performance of the proposed model in the two particular cases presented.