Characterizations and Infinite Divisibility of Certain Recently Introduced Distributions IV

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future

Generalized Transmuted Family of Distributions: Properties and Applications

We introduce and study general mathematical properties of a new generator of continuous distributions with two extra parameters called the Generalized Transmuted Family of Distributions. We investigate the shapes and present some special models. The new density function can be expressed as a linear combination of exponentiated densities in terms of the same baseline distribution. We obtain explicit expressions for the ordinary and incomplete moments and generating function, Bonferroni and Lorenz curves, asymptotic distribution of the extreme values, Shannon and R´enyi entropies and order statistics, which hold for any baseline model. Further, we introduce a bivariate extension of the new family. We discuss the different methods of estimation of the model parameters and illustrate the potential application of the model via real data. A brief simulation for evaluating Maximum likelihood estimator is done. Finally certain characterziations of our model are presented

Classes of Ordinary Differential Equations Obtained for the Probability Functions of Exponentiated Generalized Exponential Distribution

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODE) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the exponentiated generalized exponential distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions and can serve an alternative to approximatio

Classes of Ordinary Differential Equations Obtained for the Probability Function of Exponentiated Pareto Distribution

In this paper, the differential calculus was used to obtain some classes of ordinary differential equations (ODEs) for the probability density function, quantile function, survival function, inverse survival function, hazard function and reversed hazard function of the exponentiated Pareto distribution. The stated necessary conditions required for the existence of the ODEs are consistent with the various parameters that defined the distribution. Solutions of these ODEs by using numerous available methods are new ways of understanding the nature of the probability functions that characterize the distribution. The method can be extended to other probability distributions and can serve as an alternative to approximation

Recent Developments in Distribution Theory: A Brief Survey and Some New Generalized Classes of distributions

The generalization of the classical distributions is an old practice and has been considered as precious as many other practical problems in statistics. These generalizations started with the introduction of the additional location, scale or shape parameters. In the last couple of years, this branch of statistics has received a great deal of attention and quite a few new generalized classes of distributions have been introduced. We present a brief survey of this branch and introduce several new families as well

The Transmuted Exponentiated Additive Weibull Distribution: Properties and Applications

A new generalization of the transmuted additive Weibull distribution is proposed by using the quadratic rank transmutation map, the so-called transmuted exponentiated additive Weibull distribution. It retains the characteristics of a good model. It is more flexible, being able to analyze more complex data; it includes twenty-seven sub-models as special cases and it is interpretable. Several mathematical properties of the new distribution as closed forms for ordinary and incomplete moments, quantiles, and moment generating function are presented, as well as the MLEs. The usefulness of the model is illustrated by using two real data sets

Transmuted Lindley-Geometric Distribution and its applications

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley geometric distribution as the base value distribution by introducing a new parameter that would offer more distributional flexibility. It will be shown that the analytical results are applicable to model real world data.Comment: 20 pages, 6 figures. arXiv admin note: substantial text overlap with arXiv:1309.326