A model for bimodal rates and proportions.

The beta model is the most important distribution for fitting data with the unit interval. However, the beta distribution is not suitable to model bimodal unit interval data. In this paper, we propose a bimodal beta distribution constructed by using an approach based on the alpha-skew-normal model. We discuss several properties of this distribution, such as bimodality, real moments, entropies and identifiability. Furthermore, we propose a new regression model based on the proposed model and discuss residuals. Estimation is performed by maximum likelihood. A Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples with a discussion of the results. An application is provided to show the modelling competence of the proposed distribution when the data sets show bimodality.

The unit generalized half-normal quantile regression model: formulation, estimation, diagnostics, and numerical applications.

In this paper, we propose and derive a new regression model for response variables defined on the open unit interval. By reparameterizing the unit generalized half-normal distribution, we get the interpretation of its location parameter as being a quantile of the distribution. In addition, we can evaluate effects of the explanatory variables in the conditional quantiles of the response variable as an alternative to the Kumaraswamy quantile regression model. The suitability of our proposal is demonstrated with two simulated examples and two real applications. For such data sets, the obtained fits of the proposed regression model are compared with that provided by a Kumaraswamy regression model.

An overview on parametric quantile regression models and their computational implementation with applications to biomedical problems including COVID-19 data.

Quantile regression allows us to estimate the relationship between covariates and any quantile of the response variable rather than the mean. Recently, several statistical distributions have been considered for quantile modeling. The objective of this study is to provide a new computational package, two biomedical applications, one of them with COVID-19 data, and an up-to-date overview of parametric quantile regression. A fully parametric quantile regression is formulated by first parameterizing the baseline distribution in terms of a quantile. Then, we introduce a regression-based functional form through a link function. The density, distribution, and quantile functions, as well as the main properties of each distribution, are presented. We consider 18 distributions related to normal and non-normal settings for quantile modeling of continuous responses on the unit interval, four distributions for continuous response, and one distribution for discrete response. We implement an R package that includes estimation and model checking, density, distribution, and quantile functions, as well as random number generators, for distributions using quantile regression in both location and shape parameters. In summary, a number of studies have recently appeared applying parametric quantile regression as an alternative to the distribution-free quantile regression proposed in the literature. We have reviewed a wide body of parametric quantile regression models, developed an R package which allows us, in a simple way, to fit a variety of distributions, and applied these models to two examples with biomedical real-world data from Brazil and COVID-19 data from US for illustrative purposes. Parametric and non-parametric quantile regressions are compared with these two data sets.

A collection of parametric modal regression models for bounded data.

Modal regression is an alternative approach for investigating the relationship between the most likely response and covariates and can hence reveal important structure missed by usual regression methods. This paper provides a collection of parametric mode regression models for bounded response variable by considering some recently introduced probability distributions with bounded support along with the well-established Beta and Kumaraswamy distribution. The main properties of the distributions are highlighted and compared. An empirical comparison between the considered modal regression is demonstrated through the analysis of three data sets from health and social science. For reproducible research, the proposed models are freely available to users as an R package unitModalReg.

A parametric quantile regression approach for modelling zero-or-one inflated double bounded data.

Over the last decades, the challenges in applied regression have been changing considerably, and full probabilistic modeling rather than predicting just means is crucial in many applications. Motivated by two applications where the response variable is observed on the unit-interval and inflated at zero or one, we propose a parametric quantile regression considering the unit-Weibull distribution. In particular, we are interested in quantifying the influence of covariates on the quantiles of the response variable. The maximum likelihood method is used for parameters estimation. Monte Carlo simulations reveal that the maximum likelihood estimators are nearly unbiased and consistent. Also, we define a residual analysis to assess the goodness of fit.

Mixture and nonmixture cure fraction models assuming discrete lifetimes: Application to a pelvic sarcoma dataset.

Different cure fraction models have been used in the analysis of lifetime data in presence of cured patients. This paper considers mixture and nonmixture models based on discrete Weibull distribution to model recurrent event data in presence of a cure fraction. The novelty of this study is the use of a discrete lifetime distribution in place of usual existing continuous lifetime distributions for lifetime data in presence of cured fraction, censored data, and covariates. In the verification of the fit of the proposed model it is proposed the use of randomized quantile residuals. An extensive simulation study is considered to evaluate the properties of the estimates of the parameters related to the proposed model. As an illustration of the proposed methodology, it is considered an application considering a medical dataset related to lifetimes in a retrospective cohort study conducted by Puchner et al. (2017) that consists of 147 consecutive cases with surgical treatment of a sarcoma of the pelvis between the years of 1980 and 2012.