Essays on distribution theory: recent generators
In this presentation, we characterize some extended classes of distributions recently proposed in the statistical literature, videlicet Gamma-G (Zografos and Balakrishnan, 2009), Generalized Transmuted-G (Alizadeh el al., 2016), Exponentiated generalized-G (Cordeiro et al., 2013) and A new -power transformation-G (Mahavi and Kundu, 2017). Several properties of these extended classes and some special cases are discussed, such as quantile function, ordinary and incomplete moments and moment generating function. Here, we obtain generalizations of the four distributions known in the literature: Birnbaum-Sunders (Birnbaum and Saunders, 1969), Exponential (very important model sinceit describes the time between events in a Poisson process and it is found in various contexts), Normal (see Laplace (1778), Adrain (1808) and Gauss (1809), for example) and Nadarajah-Haghighi (Nadarajah and Haghighi, 2011). The model parameters are estimated by maximum likelihood and the usefulness of the new distributions is illustrated by means of a simulation study and applications to real data sets.