Hacettepe University, Department of Mathematics
Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics
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.
Alizadeh, Morad; Merovci, Faton; and Hamedani, Gholamhossein G., "Generalized Transmuted Family of Distributions: Properties and Applications" (2016). Mathematics, Statistics and Computer Science Faculty Research and Publications. 617.
Published version. Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics, Vol. 46, No. 4 (January 2016):645-668. DOI. © 2016 Hacettepe University. Used with permission.