Search

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, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

This article presents an extended distribution that builds upon the exponential distribution. This extension is based on a scale mixture between the exponential and beta distributions. By utilizing this approach, we obtain a distribution that offers increased flexibility in terms of the kurtosis coefficient. We explore the general density, properties, moments, asymmetry, and kurtosis coefficients of this distribution. Statistical inference is performed using both the moments and maximum likelihood methods. To show the performance of this new model, it is applied to a real dataset with atypical observations. The results indicate that the new model outperforms two other extensions of the exponential distribution. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new continuous distribution based on the unit interval. This distribution is generated from a transformation of a random variable with half-normal distribution. We study its basic properties, percentiles, moments and order statistics. Maximum likelihood estimation is applied, and we present a simulation study to observe the behavior of the maximum likelihood estimators. We examine two applications to real proportions datasets, where the new distribution is shown to provide a better fit than other distributions defined in the unit interval. [ABSTRACT FROM AUTHOR]

In this paper, we extend the Lomax–Rayleigh distribution to increase its kurtosis. The construction of this distribution is based on the idea of the Slash distribution, that is, its representation is based on the quotient of two independent random variables, one being a random variable with a Lomax–Rayleigh distribution and the other a beta (q , 1) . Based on the representation of this family, we study its basic properties, such as moments, coefficients of skewness, and kurtosis. We perform statistical inference using the methods of moments and maximum likelihood. To illustrate this methodology, we apply it to two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, a new family of continuous distributions with positive support is introduced. This family is generated by a truncation of the family of univariate symmetrical distributions. In this new family of distributions, general properties, such as moments, asymmetry and kurtosis coefficients, are derived. Particular cases of interest based on the normal, logistic, Laplace and Cauchy models are discussed in depth. The estimation of parameters is carried out by applying moments and maximum likelihood methods. Also, a simulation study was conducted to illustrate the good performance of estimators. An application to the Survival Times (in days) of Guinea Pigs dataset is included, where the special cases of distributions in this family are fitted. The option which provides the best fit is ultimately chosen. An R package, called "tpn", has been implemented, which includes the relevant cases of interest in this family. [ABSTRACT FROM AUTHOR]

The slash-weighted Lindley model is introduced due to the need to obtain a model with more kurtosis than the weighted Lindley distribution. Several expressions for the pdf of this model are given. Its cumulative distribution function is expressed in terms of a generalized hypergeometric function and the incomplete gamma function. Moments and maximum likelihood estimation were studied. A simulation study was carried out to illustrate the good performance of the estimates. Finally, two real applications are included. [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 article introduces a bimodal model based on the epsilon-skew-normal distribution. This extension generates bimodal distributions similar to those produced by the mixture of normal distributions. We study the basic properties of this new family. We apply maximum likelihood estimators, calculate the information matrix and present a simulation study to assess parameter recovery. Finally, we illustrate the results to three real data sets, suggesting this new distribution as a plausible alternative for modelling bimodal data. [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 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. [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]

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. [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]

In the paper, we present an extension of the truncated-exponential skew-normal (TESN) distribution. This distribution is defined as the quotient of two independent random variables whose distributions are the TESN distribution and the beta distribution with shape parameters q and 1, respectively. The resulting distribution has a more flexible coefficient of kurtosis. We studied the general probability density function (pdf) of this distribution, its survival and hazard functions, some of its properties, moments and inference by the maximum likelihood method. We carried out a simulation and applied the methodology to a real dataset. [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]

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]

This article proposes a new distribution, the Confluent hypergeometric slashed-Rayleigh distribution. The new distribution can be seen as an alternative to the slashed-Rayleigh distribution. It arises as quotient of two independent random variables, one being a Rayleigh distribution in the numerator the other a square root of the beta distribution in the denominator. Several structural properties (such as the density function, hazard rate function and moments) are derived. Parameters estimation is performed based on the moment and maximum likelihood methods. Finally, two applications are presented in which the utility of the new model in the analysis of real data is illustrated. [ABSTRACT FROM AUTHOR]