Abstract: For the first time, we propose and study the Kumaraswamy generalized half-normal distribution for modeling skewed positive data. The half-normal and generalized half-normal (Cooray and Ananda, 2008) distributions are special cases of the new model. Various of its structural properties are derived, including explicit expressions for the density function, moments, generating and quantile functions, mean deviations and moments of the order statistics. We investigate maximum likelihood estimation of the parameters and derive the expected information matrix. The proposed model is modified to open the possibility that long-term survivors may be presented in the data. Its applicability is illustrated by means of four real data sets.
The normal distribution is the most popular model in applications to real data. We propose a new extension of this distribution, called the Kummer beta normal distribution, which presents greater flexibility to model scenarios involving skewed data. The new probability density function can be represented as a linear combination of exponentiated normal pdfs. We also propose analytical expressions for some mathematical quantities: Ordinary and incomplete moments, mean deviations and order statistics. The estimation of parameters is approached by the method of maximum likelihood and Bayesian analysis. Likelihood ratio statistics and formal goodnessof-fit tests are used to compare the proposed distribution with some of its sub-models and non-nested models. A real data set is used to illustrate the importance of the proposed model.
The Birnbaum-Saunders generalized t (BSGT) distribution is a very flflexible family of distributions that admits different degrees of skewness and kurtosis and includes some important special or limiting cases available in the literature, such as the Birnbaum-Saunders and BirnbaumSaunders t distributions. In this paper we provide a regression type model to the BSGT distribution based on the generalized additive models for location, scale and shape (GAMLSS) framework. The resulting model has high flflexibility and therefore a great potential to model the distribution parameters of response variables that present light or heavy tails, i.e. platykurtic or leptokurtic shapes, as functions of explanatory variables. For different parameter settings, some simulations are performed to investigate the behavior of the estimators. The potentiality of the new regression model is illustrated by means of a real motor vehicle insurance data set.
Abstract: A new extension of the generalized gamma distribution with six parameter called the Kummer beta generalized gamma distribution is introduced and studied. It contains at least 28 special models such as the beta generalized gamma, beta Weibull, beta exponential, generalized gamma, Weibull and gamma distributions and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of generalized gamma densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, generating function, mean deviations, entropy, density function of the order statistics and their moments are derived. The elements of the observed information matrix are provided. We discuss the method of maximum likelihood and a Bayesian approach to fit the model parameters. The superiority of the new model is illustrated by means of three real data sets.
Football, or soccer, is considered one of the most important col- lective sports in the world. Managers, specialists and fans are always trying to find out the important keys to have a good team. The evaluation of the team quality may present many variables and subjective concepts, and for this reason, it is not simple to answer the following question: How to define quality? Another point that should be considered is the importance of aspects such as offensive and defensive: Which one is more important to measure quality of a football team? For this task, we propose the use of a causal model with latent variables as a tool to measure the subjectivity of the team quality and how it can be affected by other aspects. Information from the four most important football leagues in the world (England, Germany, Italy and Spain) during three seasons (2011-2012; 2012-2013; 2013-2014) was collected. We defined the latent variables in the model and evaluated the relationships among them. The results show that the offensive aspect exert more influence on team quality than defensive aspect, which reflects directly on the players market strategies.
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.