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The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution. [ABSTRACT FROM AUTHOR]

In this paper, the scale mixture of the Gleser (SMG) distribution is introduced. This new distribution is the product of a scale mixture between the Gleser (G) distribution and the Beta (a , 1) distribution. The SMG distribution is an alternative to distributions with two parameters and a heavy right tail. We study its representation and some basic properties, maximum likelihood inference, and Fisher's information matrix. We present an application to a real dataset in which the SMG distribution shows a better fit than two other known distributions. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonlinear regression model with exponentiated skew-elliptical errors distributed, which can be fitted to datasets with high levels of asymmetry and kurtosis. Maximum likelihood estimation procedures in finite samples are discussed and the information matrix is deduced. We carried out a diagnosis of the influence for the nonlinear model. To analyze the sensitivity of the maximum likelihood estimators of the model's parameters to small perturbations in distribution assumptions and parameter estimation, we studied the perturbation schemes, the case weight, and the explanatory and response variables of perturbations; we also carried out a residual analysis of the deviance components. Simulation studies were performed to assess some properties of the estimators, showing the good performance of the proposed estimation procedure in finite samples. Finally, an application to a real dataset is presented. [ABSTRACT FROM AUTHOR]

This paper presents a new distribution, the product of the mixture between Maxwell-Boltzmann and a particular case of the generalized gamma distributions. The resulting distribution, called the Scale Mixture Maxwell-Boltzmann, presents greater kurtosis than the recently introduced slash Maxwell-Boltzmann distribution. We obtained closed-form expressions for its probability density and cumulative distribution functions. We studied some of its properties and moments, as well as its skewness and kurtosis coefficients. Parameters were estimated by the moments and maximum likelihood methods, via the Expectation-Maximization algorithm for the latter case. A simulation study was performed to illustrate the parameter recovery. The results of an application to a real data set indicate that the new model performs very well in the presence of outliers compared with other alternatives in the literature. [ABSTRACT FROM AUTHOR]

This work presents an extension of the slash Lindley–Weibull distribution, of which it can be considered a modification. The new family is obtained by using the quotient of two independent random variables: a two-parameter Lindley–Weibull distribution divided by a power of the exponential distribution with parameter equal to 2. We present the pdf and cdf of the new distribution, analyzing their risk functions. Some statistical properties are studied and the moments and coefficients of asymmetry and kurtosis are shown. The parameter estimation problem is carried out by the maximum likelihood method. The method is assessed by a Monte Carlo simulation study. We use nutrition data, which are characterized by high kurtosis, to illustrate the usefulness of the proposed model. [ABSTRACT FROM AUTHOR]

In actuarial statistics, distributions with heavy tails are of great interest to actuaries, as they represent a better description of risk exposure through a type of indicator with a certain probability. These risk indicators are used to determine companies' exposure to a particular risk. In this paper, we present a distribution with heavy right tail, studying its properties and the behaviour of the tail. We estimate the parameters using the maximum likelihood method and evaluate the performance of these estimators using Monte Carlo. We analyse one set of simulated data and another set of real data, showing that the distribution studied can be used to model income data. [ABSTRACT FROM AUTHOR]

In this paper, we introduce bimodal extensions, one symmetric and one asymmetric, of the logistic distribution. We define this new density and study some basic properties. We draw inferences from the moment estimator and maximum likelihood approaches. We present a simulation study to assess the behaviour of the moment and maximum likelihood estimators. We also study the singularity of the Fisher information matrix for particular cases. We offer applications in real data and compare them with a mixture of logistics distributions. [ABSTRACT FROM AUTHOR]

In this paper, an extension of the power half-normal (PHN) distribution is introduced. This new model is built on the application of slash methodology for positive random variables. The result is a distribution with greater kurtosis than the PHN; i.e., its right tail is heavier than the PHN distribution. Its probability density, survival and hazard rate function are studied, and moments, skewness and kurtosis coefficientes are obtained, along with relevant properties of interest in reliability. It is also proven that the new model can be expressed as the scale mixture of a PHN and a uniform distribution. Moreover, the new model holds the PHN distribution as a limit case when the new parameter tends to infinity. The parameters in the model are estimated by the method of moments and maximum likelihood. A simulation study is given to illustrate the good behavior of maximum likelihood estimators. Two real applications to survival and fatigue fracture data are included, in which our proposal outperforms other models. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an extension of the sinh Cauchy distribution including a double regression model for both the quantile and scale parameters. This model can assume different shapes: unimodal or bimodal, symmetric or asymmetric. We discuss some properties of the model and perform a simulation study in order to assess the performance of the maximum likelihood estimators in finite samples. A real data application is also presented. [ABSTRACT FROM AUTHOR]

This article introduces an extension of the Power Muth (PM) distribution for modeling positive data sets with a high coefficient of kurtosis. The resulting distribution has greater kurtosis than the PM distribution. We show that the density can be represented based on the incomplete generalized integro-exponential function. We study some of its properties and moments, and its coefficients of asymmetry and kurtosis. We apply estimations using the moments and maximum likelihood methods and present a simulation study to illustrate parameter recovery. The results of application to two real data sets indicate that the new model performs very well in the presence of outliers. [ABSTRACT FROM AUTHOR]

In this paper we introduce a distribution which is an extension of the power Maxwell distribution. This new distribution is constructed based on the quotient of two independent random variables, the distributions of which are the power Maxwell distribution and a function of the uniform distribution (0,1) respectively. Thus the result is a distribution with greater kurtosis than the power Maxwell. We study the general density of this distribution, and some properties, moments, asymmetry and kurtosis coefficients. Maximum likelihood and moments estimators are studied. We also develop the expectation–maximization algorithm to make a simulation study and present two applications to real data. [ABSTRACT FROM AUTHOR]

In this article, we study an extension of the sinh Cauchy model in order to obtain asymmetric bimodality. The behavior of the distribution may be either unimodal or bimodal. We calculate its cumulative distribution function and use it to carry out quantile regression. We calculate the maximum likelihood estimators and carry out a simulation study. Two applications are analyzed based on real data to illustrate the flexibility of the distribution for modeling unimodal and bimodal data. [ABSTRACT FROM AUTHOR]