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Irving W. Burr pioneered the introduction of the Burr XII model which is commonly used in reliability and medical studies. Based on this distribution, we propose a new model called the odd-log-logistic Burr XII distribution for describing lifetime data. It contains several special models such as the log-logistic, Weibull and Burr XII distributions, among several others and thus could be a better model for analyzing positive skewed data. The new density function can be expressed as a linear combination of Burr XII densities. Various mathematical properties of the new distribution including explicit expressions for the ordinary and incomplete moments, cumulants and generating function are derived. We discuss the method of maximum likelihood to fit the model parameters for censored data. For different parameter settings and sample sizes, various simulation cenarious are performed and compared in order to study the performance of the new distribution. The superiority of the proposed lifetime model is illustrated by means of two real data sets. [ABSTRACT FROM AUTHOR]

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We introduce a new class of distributions called the Weibull Marshall–Olkin-G family. We obtain some of its mathematical properties. The special models of this family provide bathtub-shaped, decreasing-increasing, increasing-decreasing-increasing, decreasing-increasing-decreasing, monotone, unimodal and bimodal hazard functions. The maximum likelihood method is adopted for estimating the model parameters. We assess the performance of the maximum likelihood estimators by means of two simulation studies. We also propose a new family of linear regression models for censored and uncensored data. The flexibility and importance of the proposed models are illustrated by means of three real data sets. [ABSTRACT FROM AUTHOR]

We propose a new cure rate survival model by assuming that the initial number of competing causes of the event of interest follows a Poisson distribution and the time to event has the odd log-logistic generalized half-normal distribution. This survival model describes a realistic interpretation for the biological mechanism of the event of interest. We estimate the model parameters using maximum likelihood. For different sample sizes, various simulation scenarios are performed. We propose the diagnostics and residual analysis to verify the model assumptions. The potentiality of the new cure rate model is illustrated by means of a real data. [ABSTRACT FROM AUTHOR]

We introduce a new flexible distribution to deal with variables on the unit interval based on a transformation of the sinh-arcsinh distribution, which accommodates different degrees of skewness and kurtosis and becomes an interesting alternative to model this type of data. We also include this new distribution into the generalised additive models for location, scale and shape (GAMLSS) framework in order to develop and fit its regression model. For different parameter settings, some simulations are performed to investigate the behaviour of the estimators. The potentiality of the new regression model is illustrated by means of a real dataset related to the points rate of football teams at the end of a championship from the four most important leagues in the world: Barclays Premier League (England), Bundesliga (Germany), Serie A (Italy) and BBVA league (Spain) during three seasons (2011-2012, 2012-2013 and 2013-2014). [ABSTRACT FROM AUTHOR]

Cooray and Ananda (2008) pioneered a lifetime model commonly used in reliability studies. Based on this distribution, we propose a new model called the odd log-logistic generalized half-normal distribution for describing fatigue lifetime data. Various of its structural properties are derived. We discuss the method of maximum likelihood to fit the model parameters. For different parameter settings and sample sizes, some simulation studies compare the performance of the new lifetime model. It can be very useful, and its superiority is illustrated by means of a real dataset. [ABSTRACT FROM PUBLISHER]

Football, or soccer, is considered one of the most important collective 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. [ABSTRACT FROM AUTHOR]

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 Birnbaum-Saunders 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 FROM AUTHOR]

We introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7]. Some of its structural properties including explicit expressions for the density function, quantile and generating functions and ordinary moments are derived. We estimate the model parameters by the maximum likelihood method. For different parameter settings, proportion of censoring and sample size, some simulations are performed to investigate the behavior of the estimators. We derive the appropriate matrices for assessing local influence diagnostics on the parameter estimates under different perturbation schemes. We also define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. In addition, we demonstrate that the extended regression model can be very useful in the analysis of real data and provide more realistic fits than other special regression models. The potentiality of the new regression model is illustrated by means of a real data set. [ABSTRACT FROM PUBLISHER]

The gamma distribution has been widely used in many research areas such as engineering and survival analysis. We present an extension of this distribution, called the Kummer beta gamma distribution, having greater flexibility to model scenarios involving skewed data. We derive analytical expressions for some mathematical quantities. The estimation of parameters is approached by the maximum likelihood method and Bayesian analysis. The likelihood ratio and formal goodness-of-fit tests are used to compare the presented distribution with some of its sub-models and non nested models. A real data set is used to illustrate the importance of the distribution. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We formulate and study a four-parameter lifetime model called the beta extended half-normal distribution. This model includes as sub-models the exponential, extended half-normal and half-normal distributions. We derive expansions for the new density function which do not depend on complicated functions. We obtain explicit expressions for the moments and incomplete moments, generating function, mean deviations, Bonferroni and Lorenz curves and Rényi entropy. In addition, the model parameters are estimated by maximum likelihood. We provide the observed information matrix. The new model is modified to cope with possible long-term survivors in the data. The usefulness of the new distribution is shown by means of two real data sets. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]