We introduce a new class of distributions called the Burr XII system of densities with two extra positive parameters. We provide a comprehensive treatment of some of its mathematical properties. We estimate the model parameters by maximum likelihood. We assess the performance of the maximum likelihood estimators in terms of biases and mean squared errors by means of a simulation study. We also introduce a new family of regression models based on this system of densities. The usefulness of the proposed models is illustrated by means of three real data sets.

In this study, we introduce a new family of continuous distributions with one extra shape parameter, called the Burr-Hatke-G family, based on the Burr-Hatke differential equation. Some of its mathematical properties are derived. The maximum likelihood method is used to estimate the model parameters. Moreover, the log-Burr-Hatke-Weibull regression model based on new the generated family is introduced. The usefulness of the proposed family is demonstrated by means of the three real data applications. Empirical results indicate that the proposed family provides more realistic fits than other well-known family of distributions.

We propose a generalized Weibull family of distributions with two extra positive parameters to extend the normal, gamma, Gumbel and inverse Gausssian distributions, among several other well-known distributions. We provide a comprehensive treatment of its general mathematical properties including quantile and generating functions, ordinary and incomplete moments and other properties. We introduce the log-generalized Weibull-log-logistic, this is new regression model represents a parametric family of models that includes as sub-models several widely known regression models that can be applied to censored survival data. We discuss estimation of the model parameters by maximum likelihood and provide two applications to real data.

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.

One of the key features in regression models consists in selecting appropriate characteristics that explain the behavior of the response variable, in which stepwise-based procedures occupy a prominent position. In this paper we performed several simulation studies to investigate whether a specific stepwise-based approach, namely Strategy A, properly selects authentic variables into the generalized additive models for location, scale and shape framework, considering Gaussian, zero inflated Poisson and Weibull distributions. Continuous (with linear and nonlinear relationships) and categorical explanatory variables are considered and they are selected through some goodness-of-fit statistics. Overall, we conclude that the Strategy A greatly performed.