Journal of Data Science

Abstract: In this paper the log-exponentiated-Weibull regression model is modified to allow the possibility that long term survivors are present in the data. The modification leads to a log-exponentiated-Weibull regression model with cure rate, encompassing as special cases the log-exponencial regression and log-Weibull regression models with cure rate typically used to model such data. The models attempt to estimate simultaneously the effects of covariates on the acceleration/deceleration of the timing of a given event and the surviving fraction; that is, the proportion of the population for which the event never occurs. Assuming censored data, we consider a classic analysis and Bayesian analysis for the parameters of the proposed model. The normal curvatures of local influence are derived under various perturbation schemes and two deviance-type residuals are proposed to assess departures from the log-exponentiated-Weibull error assumption as well as to detect outlying observations. Finally, a data set from the medical area is analyzed.

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.

Abstract: In this paper, we propose a flexible cure rate survival model by as suming that the number of competing causes of the event of interest follows the negative binomial distribution and the time to event follows a generalized gamma distribution. We define the negative binomial-generalized gamma distribution, which can be used to model survival data. The new model in cludes as special cases some of the well-known cure rate models discussed in the literature. We consider a frequentist analysis and nonparametric boot strap for parameter estimation of a negative binomial-generalized gamma regression model with cure rate. Then, we derive the appropriate matri ces for assessing local influence on the parameter estimates under different perturbation schemes and present some ways to perform global influence analysis. Finally, we analyze a real data set from the medical area.

Abstract: We propose a new method of adding two parameters to a contin uous distribution that extends the idea first introduced by Lehmann (1953) and studied by Nadarajah and Kotz (2006). This method leads to a new class of exponentiated generalized distributions that can be interpreted as a double construction of Lehmann alternatives. Some special models are dis cussed. We derive some mathematical properties of this class including the ordinary moments, generating function, mean deviations and order statis tics. Maximum likelihood estimation is investigated and four applications to real data are presented.