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In this paper, we present an extension of the Two-parameter Weibull distribution to make it even more flexible in terms of its kurtosis coefficient. Properties involving moments and asymmetry and kurtosis indexes are studied. Simulation studies for some cases, illustrating the usefulness of the extension considered, are carried out.En este artículo se presenta una extensión de la distribución Weibull de dos parámetros, con el objetivo de flexibilizar el modelo en términos de la kurtosis. Se estudian las propiedades básicas de la nueva densidad obtenida, así como su función de distribución, momentos, coeficientes de asimetría y kurtosis. Se realizan estudios de simulación para algunos casos particulares, ilustrando la utilidad de la extensión considerada.

In this paper a new approach is considered for studying the triangular distribution using the theoretical development behind Skew distributions. Triangular distribution are obtained by a reparametrization of usual triangular distribution. Main probabilistic properties of the distribution are studied, including moments, asymmetry and kurtosis coefficients, and an stochastic representation, which provides a simple and efficient method for generating random variables. Moments estimation is also implemented. Finally, a simulation study is conducted to illustrate the behavior of the estimation approach proposed.En este trabajo se considera un nuevo enfoque para el estudio de la distribución triangular usando el desarrollo teórico detrás de las distribuciones Skew. La distribución triangular aquí entregada se obtiene por reparametrización de la distribución triangular usual. Se estudian las principales propiedades probabilísticas, incluidos los momentos, coeficientes de asimetría y kurtosis; además, se muestra una representación estocástica para el modelo estudiado, que proporciona un método sencillo y eficiente para la generación de variables aleatorias. Así mismo, se implementa la estimación por el método de los momentos y, a través de un estudio de simulación, se ilustra el comportamiento de las estimaciones de los parámetros.

In this study, we present a new family of distributions through generalization of the extended bimodal-normal distribution. This family includes several special cases, like the normal, Birnbaum-Saunders, Student’s t, and Laplace distribution, that are developed and defined using stochastic representation. The theoretical properties are derived, and easily implemented Monte Carlo simulation schemes are presented. An inferential study is performed for the Laplace distribution. We end with an illustration of two real data sets. [ABSTRACT FROM AUTHOR]

Attention is focussed on a truncated version of the extended two-piece skew-normal distribution, studied by Arnold et al. [On multiple constraint skewed models. Statistics. 2009;3(3):279–293]. When the truncation point is set equal to zero, the resulting model can be viewed as a flexible extension of the half-normal model. Properties of the truncated distribution are investigated and corresponding likelihood inference is considered. The methodology is applied to data set involving non-negative observations and it is verified that the fit of the truncated model compares favourably with that of the half-normal. [ABSTRACT FROM AUTHOR]

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The main object of this paper is to develop an alternative construction for the bimodal skew-normal distribution. The construction is based upon a study of the mixture of skew-normal distributions. We study some basic properties of this family, its stochastic representations and expressions for its moments. Parameters are estimated using the maximum likelihood estimation method. A simulation study is carried out to observe the performance of the maximum likelihood estimators. Finally, we compare the efficiency of the new distribution with other distributions in the literature using a real data set. The study shows that the proposed approach presents satisfactory results. [ABSTRACT FROM AUTHOR]