Revista de Matemáticas 17(2)

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  • Ítem
    An Alternative to Chaid Segmentation Algorithm Based on Entropy.
    (2010-07-02 00:00:00) Galindo Villardón, María Purificación; Vicente Villardón, José Luis; Dorado Díaz, Ana; Vicente Galindo, María Purificación; Patino Alonso, María Carmen
    The CHAID (Chi-Squared Automatic Interaction Detection) treebased segmentation technique has been found to be an effective approach for obtaining meaningful segments that are predictive of a K-category (nominal or ordinal) criterion variable. CHAID was designed to detect, in an automatic way, the  nteraction between several categorical or ordinal predictors in explaining a categorical response, but, this may not be true when Simpson’s paradox is present. This is due to the fact that CHAID is a forward selection algorithm based on the marginal counts. In this paper we propose a backwards elimination algorithm that starts with the full set of predictors (or full tree) and eliminates predictors progressively. The elimination procedure is based on Conditional Independence contrasts using the concept of entropy. The proposed procedure is compared to CHAID.
  • Ítem
    Principal Component and Regression Analysis for Categorical Data.Application to Arterial Hypertension.
    (2010-07-02 00:00:00) Navarro Céspedes, Juan M.; Casas Cardoso, Gladys M.; González Rodríguez, Emilio
    The present work is about the statistical processing of categorical data. The mathematical details of the Categorical Principal Components and the Categorical Regression Analysis are explained.The combination of both techniques can be used to solve classification problems. Because these techniques are relatively new, we decided to use another technique (classification trees following the chi squared criteria) to make a comparison of their results, with the help of the theory of ROC curves. In the application, supposedly healthy patients of Santa Clara, Cuba, were diagnosed as hypertensive, pre hypertensive and no hypertensive by a Committee of Medical Experts. Categorical Component Analysis and Categorical Regression Analysis were applied in order to successfully solve the classification problem.
  • Ítem
    Structural Change Analysis in Linear Regression Model.
    (2010-07-02 00:00:00) Pérez Salvador, Blanca Rosa; García Salazar, María Guadalupe
    Assuming that the observations are from normal distribution we obtain de distribution of the maximum likelihood ratio test if there is a change in the parameters at an unknown time and we find the maximum likehood estimators of the time change too.
  • Ítem
    Parameter Estimation in HIV/AIDS Epidemiological Models.
    (2010-07-02 00:00:00) Barrios Ginart, Jorge; Marrero Severo, Aymée de los Ángeles; Díaz Romañach, Marta Lourdes Baguer; de Arazoza Rodríguez, Héctor
    The validation process of mathematical models that describe practical applications usually implies the estimation of the unknown parameters that are involved. In this work, in order to estimates these parameters in the HIV/AIDS models of [7], the problem of estimatingthe parameters in first order ordinary differential equations with known start point is formulated and a strategy of solution is presented. It is verified as well, which is the model of HIV/AIDS that represents best the real data according with the strategy of solution.
  • Ítem
    Limit Theorems in Bellman–Harris Processes with Finites Second Moments
    (2010-07-02 00:00:00) Llinás Solano, Humberto
    In this article are studied different theorems limits in a criticalBellman-Harris branching process with a only type of particle and with finite second moments. There were used two processes in order to figure out the limits as following as: “The condition of no extinction” and “The condition of extinction in the near future”. In the two previous processes is taken into account two different cases as: $i := dit$  y $i := di ± \tau $, where t is a point of time and $d_i\varepsilon (0,\infty )$ are fixed for every $i = 1, . . . ,k$. For the case where $i := di\tau$, the Esty’s comparison lemma 2.3 is used to investigate the asymptotic behavior of the joint probability generating function F$F(s_1,...,\tau_k)$, for $t\longrightarrow \infty $; for the case  $i := \tau + di$ is not used. For this last case is founded another comparison lemma (lemma 4.3), that is the base to demonstrate the theorems limits if $i := \tau ± di$.
  • Ítem
    Simulated Annealing–Golden section algorithm for the multiproduct replenishment problem with stochastic demand.
    (2010-07-02 00:00:00) Hernández González, Salvador; Gutiérrez Andrade, Miguel Ángel; de los Cobos Silva, Sergio Gerardo
    The joint replenishment problem (JRP) has been studied for over 30 years and there are both heuristic and exact algorithms to determine the frequency of orders and fundamental cycle; in recent years ithas been considered the model with stochastic demand. If we assume a behavior of normal distribution for the demand, we may obtain a non linear mixed-integer programming for costs, for which only is reported one heuristic solving method. In this paper we propose a simulated annealing algorithm with golden section for one-dimensional search in order to solve the JRP considering a normal distribution demand. Its performance is compared with the reported heuristic method. The results showed that the new algorithm obtains lower costs.