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Bimodal data sets are very common in different areas of knowledge. The crude birth rates data, fish length data, egg diameter data, the eruption and interruption times of the Old Faithful geyser, are examples of this type of data. In this paper, a new class of symmetric density functions for modeling bimodal data as described above are presented. From density functions with support on [ 0 , + ∞ ) , the symmetry is getting by reflecting the density function in the negative semi-axis with their respective normalization. In this way, if the primitive density function is unimodal, then the resulting density will be bimodal. We introduce asymmetry parameters and study their behavior, in particular the values of their modes and some other statistical values of interest. The cases for densities generated by Gamma, Weibull, Log-normal, and Birnbaum-Saunders densities, among others are studied. Statistical inference is performed from a classical perspective. A small simulation study to evaluate the benefits and limitations of the new proposal. In addition, an application to a data set related to the fetal weight in grams obtained through ultrasound in a sample of 500 units is also presented; the results show the great usefulness of the model in practical situations.

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This paper introduce two new families of distributions that allow fitting unimodal, bimodal or trimodal data sets. Statistical properties such as distribution function, moments, moment generating function and stochastic representation of these new families are studied in details. The problem of estimating parameters is addressed by considering the maximum likelihood method and Fisher information matrices are derived. A small Monte Carlo simulation study is conducted to examine the performance of the obtained estimators. The methodology developed is illustrated with three real data applications.

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In this paper, we propose the power Student-t regression model for censored (limited) observations which extends the Student-t censored regression model. This extension is based on the asymmetric and heavy-tailed power Student-t distribution. The score functions and expected information matrix are given as well as the process for estimating the parameters in the model is discussed by using the likelihood approach. Two simulation studies are conducted to evaluate parameter recovery and properties of the model and finally, two applications to a real data set are reported to demonstrate the usefulness of this new methodology.

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El lactosuero acidificado espontáneamente pone en riesgo la salud del consumidor al utilizarlo como acidificante de la leche usada en la elaboración del queso tipo mozzarella, y además reduce la calidad del producto. El objetivo de esta investigación fue evaluar el proceso de fermentación del lactosuero ácido (entero y desproteinizado) con Lactobacillus casei, utilizando diferentes porcentajes de su inóculo. Se caracterizaron fisicoquímicamente los lactosueros, sometiéndolos a fermentación anaeróbica a 37°C y 120 rpm por 96 h. Se evaluó la concentración de biomasa celular, el consumo de lactosa, la producción de ácido láctico (AL) y se estimaron los parámetros cinéticos y estequiométricos. Se aplicó un diseño experimental completamente al azar con arreglo factorial 2x3, empleando la metodología de medidas repetidas. Los datos, se procesaron a través de los paquetes estadísticos SAS® versión 9 y Statgraphics Centurión XVI®. El lactosuero, entero y desproteinizado, se encontró dentro de los intervalos fisicoquímicos aceptables para su acidificación. Los valores de acidez fueron superiores a 120 Grados Dornic (120°D) con la inoculación de L. casei, excepto en lactosuero desproteinizado, inoculado con 15% de cultivo. El lactosuero entero con 15% de inóculo, alcanzo 120°D en el menor tiempo (34h). Altas concentraciones de inóculo (15%) favorecieron la acidificación en el lactosuero entero, mostrando la mayor producción (20.83gAL/l), Y´p/s=0.86, Qp=0.173gAL/l*h; mientras el lactosuero desproteinizado mostró un mayor crecimiento microbiano, menor conversión de lactosa (8.2%) y menor producción media de ácido láctico (8.19g/l).

The spontaneously acidified whey threatens consumer health and reduces quality of mozzarella cheese. The goal of this research was to evaluate the acidification process of acid whey (whole and deproteinized) by fermentation with different inoculum concentrations of Lactobacillus casei. The whey was physicochemically characterized and anaerobically fermented at 37°C and120 rpm during 96h. Cellular biomass was evaluated, as well as lactose consumption, lactic acid production, kinetic and stoichiometric parameters were estimated. A completely randomized design with factorial arrangement (2x3) was applied by using the repeated measures methodology. Data was processed by using SAS® statistical package, version 9 and Statgraphics Centurion XVI®. The acidification for the whole and deproteinized whey was found within the acceptable intervals. Acidification values were above 120 degrees Dornic (120°D) with L. casei inoculation, except in the deproteinized whey inoculated with 15% of inoculum. The whole whey with 15% of inoculum reached 120°D in the shortest time (34 hours). High concentrations of inoculum (15%) aided the acidification in whole whey and showed the highest production (20.83 g LA/l), and p/s=0.86, Qp=0.173 g AL/l*h; on the other hand, the deproteinized whey showed the highest microbial growth, lowest conversion of lactose (8.2%) and lowest lactic acid production (8.19g/l).

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We develop regression models for limited and censored data based on the mixture between the log-power-normal and Bernoulli-type distributions. A likelihood-based approach is implemented for parameter estimation and a small-scale simulation study is conducted to evaluate parameter recovery, with emphasis on bias estimation. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. A real data example, the safety and immunogenecity study of measles vaccine in Haiti, is presented to illustrate how different models can be used to fit this type of data. As shown, the asymmetric models considered seem to present the best fit for the data set under study, revealing significance of the explanatory variable sex, which is not found significant with the log-normal model.

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