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Celis, P., de la Cruz, R., Fuentes, C., & Gomez, H. W. (2021). Survival and Reliability Analysis with an EpsilonPositive Family of Distributions with Applications. Symmetry, 13(5), 908.
Abstract: We introduce a new class of distributions called the epsilonpositive family, which can be viewed as generalization of the distributions with positive support. The construction of the epsilonpositive family is motivated by the ideas behind the generation of skew distributions using symmetric kernels. This new class of distributions has as special cases the exponential, Weibull, lognormal, loglogistic and gamma distributions, and it provides an alternative for analyzing reliability and survival data. An interesting feature of the epsilonpositive family is that it can viewed as a finite scale mixture of positive distributions, facilitating the derivation and implementation of EMtype algorithms to obtain maximum likelihood estimates (MLE) with (un)censored data. We illustrate the flexibility of this family to analyze censored and uncensored data using two real examples. One of them was previously discussed in the literature; the second one consists of a new application to model recidivism data of a group of inmates released from the Chilean prisons during 2007. The results show that this new family of distributions has a better performance fitting the data than some common alternatives such as the exponential distribution.

de la Cruz, R., Salinas, H. S., & Meza, C. (2022). Reliability Estimation for StressStrength Model Based on UnitHalfNormal Distribution. Symmetry, 14(4), 837.
Abstract: Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. We propose a novel estimation procedure of stressstrength reliability in the case of two independent unithalfnormal distributions can fit asymmetrical data with either positive or negative skew, with different shape parameters. We obtain the maximum likelihood estimator of the reliability, its asymptotic distribution, and exact and asymptotic confidence intervals. In addition, confidence intervals of model parameters are constructed by using bootstrap techniques. We study the performance of the estimators based on Monte Carlo simulations, the mean squared error, average bias and length, and coverage probabilities. Finally, we apply the proposed reliability model in data analysis of burr measurements on the iron sheets.

Rubio, C. A., Asenjo, F. A., & Hojman, S. A. (2019). Quantum Cosmologies Under Geometrical Unification of Gravity and Dark Energy. Symmetry, 11(7).
Abstract: A FriedmannRobertsonWalker Universe was studied with a dark energy component represented by a quintessence field. The Lagrangian for this system, hereafter called the FriedmannRobertsonWalkerquintessence (FRWq) system, was presented. It was shown that the classical Lagrangian reproduces the usual two (second order) dynamical equations for the radius of the Universe and for the quintessence scalar field, as well as a (first order) constraint equation. Our approach naturally unified gravity and dark energy, as it was obtained that the Lagrangian and the equations of motion are those of a relativistic particle moving on a twodimensional, conformally flat spacetime. The conformal metric factor was related to the dark energy scalar field potential. We proceeded to quantize the system in three different schemes. First, we assumed the Universe was a spinless particle (as it is common in literature), obtaining a quantum theory for a Universe described by the KleinGordon equation. Second, we pushed the quantization scheme further, assuming the Universe as a Dirac particle, and therefore constructing its corresponding Dirac and Majorana theories. With the different theories, we calculated the expected values for the scale factor of the Universe. They depend on the type of quantization scheme used. The differences between the Dirac and Majorana schemes are highlighted here. The implications of the different quantization procedures are discussed. Finally, the possible consequences for a multiverse theory of the Dirac and Majorana quantized Universe are briefly considered.
