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One of the most widely known probability distributions used to explain the probabilistic behavior of positive data is the log-normal (LN). Although the LN distribution is capable of adjusting data types, it is not always fully true that the model manages to adequately model the behavior of the response of interest since in some cases, the degree of skewness and/or kurtosis of the data are greater or less than those that the LN distribution can capture. Another peculiarity of the LN distribution is that it only fits unimodal positive data, which constitutes a limitation when dealing with data that present more than one mode (bimodality). On the other hand, the log-normal model only fits unimodal positive data and in reality there are multiple applications where the behavior of materials is bimodal. To fill this gap, this paper introduces a new probability distribution that is capable of fitting unimodal or bimodal positive data with a high or low degree of skewness and/or kurtosis. The new distribution is a generalization of the LN distribution. For the new proposal, its main properties are studied and the process of estimation of the parameters involved in the model is carried out from a classical perspective using the maximum likelihood method. An important feature of this distribution is the non-singularity of the Fisher information matrix, which guarantees the use of asymptotic theory to study the properties of the parameter estimators. A Monte Carlo type simulation study is carried out to evaluate the properties of the estimators and finally, an illustration is presented with a set of data related to the concentration of nickel in soil samples, allowing to show that the proposed distribution fits extremely well in certain situations.

Abstract 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.

In this study, we consider an alternative to the log-skew-normal distribution. It is called the modified log-skew-normal distribution and introduces greater flexibility in the skewness and kurtosis parameters. We first study several of the main probabilistic properties of the new distribution, such as the computation of its moments and the non-existence of the moment-generating function. Parameter estimation by the maximum likelihood approach is also studied. This approach presents an overestimation problem in the shape parameter, which in some cases, can even be infinite. However, as we demonstrate, this problem is solved by adapting bias reduction using Firth’s approach. We also show that the modified log-skew-normal model likewise inherits the non-singularity of the Fisher information matrix of the untransformed model, when the shape parameter is null. Finally, we apply the modified log-skew-normal model to a real example related to pollution data.

This paper considers an extension for the skew-elliptical Birnbaum–Saunders model by considering the power-normal model. Some properties of this family are studied and it is shown, in particular, that the range of asymmetry and kurtosis surpasses that of the ordinary skew-normal and power[1]normal models. Estimation is dealt with by using the maximum likelihood approach. Observed and expected information matrices are derived and it is shown to be nonsingular at the vicinity of symmetry. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.

In this paper, we propose a linear regression model in which the error term follows a log-gamma-normal (LGN) distribution. The assumption of LGN distribution gives flexibility to accommodate skew forms to the left and to the right. Kurtosis greater or smaller than the normal model can also be accommodated. The regression model for censored asymmetric data is also considered (censored LGN model). Parameter estimation is implemented using the maximum likelihood approach and a small simulation study is conducted to evaluate parameter recovery. The main conclusion is that the approach is very much satisfactory for moderate and large sample sizes. Results for two applications of the proposed model to real datasets are provided for illustrative purposes.

In this article, we introduce a new family of symmetric-asymmetric distributions based on skew distributions and on the family of order statistics with proportional hazards. This new family of distributions is able to fit both unimodal and bimodal asymmetric data. Furthermore, it contains, as special cases, the symmetric distribution and the “skew-symmetric” family, and therefore the skew-normal distribution. Another interesting feature of the family is that the parameter controlling the distributional shape in bimodal cases takes values in the interval (0, 1); this is an advantage for computing maximum likelihood estimates of model parameters, which is performed by numerical methods. The practical utility of the proposed distribution is illustrated in two real data applications.

The main object of this paper is to propose a new asymmetric model more flexible than the generalized Gaussian model. The probability density function of the new model can assume bimodal or unimodal shapes, and one of the parameters controls the skewness of the model. Three simulation studies are reported and two real data applications illustrate the flexibility of the model compared with traditional proposals in the literature.

La distribución de probabilidad propuesta por Birnbaum y Sa un- ders se ha usado con bastante eficacia para modelar tiempos de falla de ma- teriales sujetos a la fátiga. En este artículo definimos una e xtensión de la distribución Birnbaum-Saunders clásica sustituyendo la d istribución normal por la distribución potencia t de Student. La nueva distribución es más flexi- ble que la distribución Birnbaum-Saunders clásica en térmi nos de asimetría y curtosis. Presentamos los estimadores de máxima verosimi litud de los pa- rámetros del modelo y su modelo de regresión asociado. El aná lisis de dos aplicaciones con datos reales revelan una superioridad del nuevo modelo con relación a otros modelos existentes en la literatura.

Regression analysis is a technique widely used in different areas of human knowledge, with distinct distributions for the error term. It is the case, however, that regression models with the error term following a bimodal distribution are not common in the literature, perhaps due to the lack of simple to deal with bimodal error distributions. In this paper, we propose a simple to deal with bimodal regression model with a symmetric-asymmetric distribution for the error term for which for some values of the shape parameter it can be bimodal. This new distribution contains the normal and skew-normal as special cases. A real data application reveals that the new model can be extremely useful in such situations.

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.

In this article we study a subfamily of the slashed-Weibull family. This subfamily can be seen as an extension of the Rayleigh distribution with more flexibility in terms of the kurtosis of distribution. This special feature makes the extension suitable for fitting atypical observations. It arises as the ratio of two independent random variables, the one in the numerator being a Rayleigh distribution and a power of the uniform distribution in the denominator. We study some probability properties, discuss maximum likelihood estimation and present real data applications indicating that the slashed-Rayleigh distribution can improve the ordinary Rayleigh distribution in fitting real data.

The present paper considers an extension of the exponential distribution based on mixtures of positive distributions. We study the main properties of this new distribution, with special emphasis on its moments, moment generator function and some characteristics related to reliability studies. We also discuss parameter estimation considering the maximum likelihood and moments approach. An application reveals that the model proposed can be very useful in fitting real data. A final discussion concludes the paper.

This paper focuses on studying a truncated positive version of the power-normal (PN) model considered in Durrans (1992). The truncation point is considered to be zero so that the resulting model is an extension of the half normal distribution. Some probabilistic properties are studied for the proposed model along with maximum likelihood and moments estimation. The model is fitted to two real datasets and compared with alternative models for positive data. Results indicate good performance of the proposed model.

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 paper we consider an extension of the half-normal distribution based on the distribution of the maximum of a random sample. It is shown that this distribution belongs to the family of beta generalized half-normal distributions. Properties of its density are investigated, maximum likelihood estimation is discussed and the Fisher information matrix is derived. A real data illustration is presented, and comparisons with alternative extensions of the half-normal distribution reveal good performance of the proposed model.

In this paper we introduce a new distribution for modeling positive data with high kurtosis. This distribution can be seen as an extension of the exponentiated Rayleigh distribution. This extension builds on the quotient of two independent random variables, one exponentiated Rayleigh in the numerator and Beta(q, 1) in the denominator with q > 0. It is called the slashed exponentiated Rayleigh random variable. There is evidence that the distribution of this new variable can be more flexible in terms of modeling the kurtosis regarding the exponentiated Rayleigh distribution. The properties of this distribution are studied and the parameter estimates are calculated using the maximum likelihood method. An application with real data reveals good performance of this new distribution.