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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 work, we propose a new bimodal distribution with support in the real line. We obtain some properties of the model, such as moments, quantiles, and mode, among others. The computational implementation of the model is presented in the tpn package of the software R. We perform a simulation study in order to assess the properties of the maximum likelihood estimators in finite samples. Finally, we present an application to a bimodal data set, where our proposal is compared with other models in the literature. [ABSTRACT FROM AUTHOR]

Receiver operating characteristic (ROC) and predictiveness curves are graphical tools to study the discriminative and predictive power of a continuous‐valued marker in a binary outcome. In this paper, a copula‐based construction of the joint density of the marker and the outcome is developed for plotting and analyzing both curves. The methodology only requires a copula function, the marginal distribution of the marker, and the prevalence rate for the model to be characterized. The adoption of the Gaussian copula and the customization of the margin for the marker are proposed for such characterization. The computation of both curves is numerically more feasible than methods that attempt to obtain one curve in terms of the other. Estimation is carried out using maximum likelihood and resampling‐based methods. Randomized quantile residuals from each conditional distribution are employed for both assessing the adequacy of the model and identifying outliers. The performance of the estimators of both curves and their underlying quantities is evaluated in simulation studies that assume different dependence structures and sample sizes. The methods are illustrated with an analysis of the level of progesterone receptor gene expression for the diagnosis and prediction of estrogen receptor‐positive breast cancer. [ABSTRACT FROM AUTHOR]

In this paper, we propose a bimodal gamma distribution using a quadratic transformation based on the alpha-skew-normal model. We discuss several properties of this distribution such as mean, variance, moments, hazard rate and entropy measures. Further, we propose a new regression model with censored data based on the bimodal gamma distribution. This regression model can be very useful to the analysis of real data and could give more realistic fits than other special regression models. Monte Carlo simulations were performed to check the bias in the maximum likelihood estimation. The proposed models are applied to two real data sets found in the literature. [ABSTRACT FROM AUTHOR]

This article proposes new symmetric and asymmetric distributions applying methods analogous as the ones in Kim (2005) and Arnold et al. (2009) to the exponentiated normal distribution studied in Durrans (1992), that we call the power-normal (PN) distribution. The proposed bimodal extension, the main focus of the paper, is called the bimodal power-normal model and is denoted byBPN(α) model, where α is the asymmetry parameter. The authors give some properties including moments and maximum likelihood estimation. Two important features of the model proposed is that its normalizing constant has closed and simple form and that the Fisher information matrix is nonsingular, guaranteeing large sample properties of the maximum likelihood estimators. Finally, simulation studies and real applications reveal that the proposed model can perform well in both situations. [ABSTRACT FROM AUTHOR]

In this article, we introduce a new extension of the Birnbaum–Saunders (BS) distribution as a follow-up to the family of skew-flexible-normal distributions. This extension produces a family of BS distributions including densities that can be unimodal as well as bimodal. This flexibility is important in dealing with positive bimodal data, given the difficulties experienced by the use of mixtures of distributions. Some basic properties of the new distribution are studied including moments. Parameter estimation is approached by the method of moments and also by maximum likelihood, including a derivation of the Fisher information matrix. Three real data illustrations indicate satisfactory performance of the proposed model. [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]