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The logistic distribution and the S-shaped pattern of its cumulative distribution and quantile functions have been extensively used in many different spheres affecting human life. By far, the most well-known application of logistic distribution is in the logistic regression that is used for modeling categorical response variables. The exponentiated-exponential logistic distribution, a generalization of the logistic distribution, is obtained using the technique proposed by Alzaatreh et al. (2013) of mixing two distributions, hereafter called the EEL distribution. This distribution subsumes various types of logistic distribution. The structural analysis of the distribution in this paper includes limiting behavior, quantiles, moments, mode, skewness, kurtosis, order statistics, the large sample distributions of the sample maximum and the sample minimum, and the distribution of the sample median. For illustrative purposes, a real-life data set is considered as an application of the EEL distribution. [ABSTRACT FROM PUBLISHER]

Selection of appropriate predictors for right censored time to event data is very often encountered by the practitioners. We consider the ℓ1penalized regression or “least absolute shrinkage and selection operator” as a tool for predictor selection in association with accelerated failure time model. The choice of the penalizing parameter λ is crucial to identify the correct set of covariates. In this paper, we propose an information theory-based method to choose λ under log-normal distribution. Furthermore, an efficient algorithm is discussed in the same context. The performance of the proposed λ and the algorithm is illustrated through simulation studies and a real data analysis. The convergence of the algorithm is also discussed. [ABSTRACT FROM AUTHOR]

Pareto distributions and their close relatives and generalizations provide very flexible families of heavy-tailed distributions that may be used to model income distributions as well as a wide variety of other social and economic distributions. On the other hand, gamma distribution has a wide application in various social and economic spheres such as survival analysis, to model aggregate insurance claims, and the amount of rainfall accumulated in a reservoir etc. Combining the above two heavy-tailed distributions, using the technique by Alzaatreh et al. (2012), we define a new distribution, namely Gamma-Pareto (IV) distribution, hereafter called asGPD(IV)distribution. Various properties of theGPD(IV)are investigated such as limiting behavior, moments, mode, and Shannon entropy. Also some characterizations of theGPD(IV)distribution are mentioned in this paper. Maximum likelihood method is proposed for estimating the model parameters. For illustrative purposes, real data sets are considered as applications of theGPD(IV)distribution. [ABSTRACT FROM AUTHOR]

In supervised learning, especially in decision tree induction, many measures are based on the concept of entropy. A major characteristic of entropies is that they take their maximal value when the distribution of the modalities of the class variable is uniform. In particular, to deal with the case when the a priori frequencies of the class variable modalities are imbalanced, we propose an off-centered entropy which takes its maximum value for a distribution fixed by the user. This distribution can be the overall distribution of the class variable or a distribution taking into account the costs of misclassification. Other authors proposed an asymmetric entropy. In this article, we propose an adaptive strategy of induction of decision trees based on these non centered entropies. The first experiments on ten data bases using the C4.5 induction tree show that both non centered entropies are promising in comparison with the classical Shannon entropy. [ABSTRACT FROM AUTHOR]

In this article, results for some well-known families such as Pareto IV, generalized logistic, generalized gamma, double generalized gamma, generalized normal, inverse gamma, and Weibull, and their related families via the links between entropy, variance, Fisher information, and analog of the Fisher information, are derived. [ABSTRACT FROM AUTHOR]

Asymptotic confidence intervals are given for two functions of multinomial outcome probabilities: Gini's diversity measure and Shannon's entropy. "Adjusted" proportions are used in all asymptotic mean and variance formulas, along with a possible logarithmic transformation. Exact confidence coe5cients are computed in some cases. Monte Carlo simulation is used in other cases to compare actual coverages to nominal ones. Some recommendations are made. [ABSTRACT FROM AUTHOR]