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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 this article we study the properties, inference, and statistical applications to a parametric generalization of the truncation positive normal distribution, introducing a new parameter so as to increase the flexibility of the new model. For certain combinations of parameters, the model includes both symmetric and asymmetric shapes. We study the model's basic properties, maximum likelihood estimators and Fisher information matrix. Finally, we apply it to two real data sets to show the model's good performance compared to other models with positive support: the first, related to the height of the drum of the roller and the second, related to daily cholesterol consumption. [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]

The Marshall-Olkin extended family of distributions is an alternative for modeling lifetimes, and considers more or less asymmetry than its parent model, achieved by incorporating just one extra parameter. We investigate the bias of maximum likelihood estimators and use it to develop an estimator with less bias than traditional estimators, by a modification of the score function. Unlike other proposals, in this paper, we consider a bias reduction methodology that can be applied to any member of the family and not necessarily to any particular distribution. We conduct a Monte Carlo simulation in order to study the performance of the corrected estimators in finite samples. This simulation shows that the maximum likelihood estimator is quite biased and the proposed estimator is much less biased; in small sample sizes, the bias is reduced by around 50 percent. Two applications, related to the air conditioning system of an airplane and precipitations, are presented to illustrate the results. In those applications, the bias reduction for the shape parameters is close to 25% and the bias reduction also reduces, among others things, the width of the 95% confidence intervals for quantiles lower than 0.594. [ABSTRACT FROM AUTHOR]