Mediterr. J. Math.
Springer International Publishing AG 2017
The Exponentiated Weibull-H Family of
Distributions: Theory and Applications
Gauss M. Cordeiro, Ahmed Z. Aﬁfy, Haitham M. Yousof,
Abstract. A new class of continuous distributions called the exponen-
tiated Weibull-H family is proposed and studied. The proposed class
extends the Weibull-H family of probability distributions introduced by
Bourguignon et al. (J Data Sci 12:53–68, 2014). Some special models of
the new family are presented. Its basic mathematical properties includ-
ing explicit expressions for the ordinary and incomplete moments, quan-
tile and generating function, R´enyi and Shannon entropies, order sta-
tistics, and probability weighted moments are derived. The maximum-
likelihood method is adopted to estimate the model parameters and a
simulation study is performed. The ﬂexibility of the generated family is
proved empirically by means of two applications to real data sets.
Mathematics Subject Classiﬁcation. Primary 60E05; Secondary 62P99.
Keywords. Weibull distribution, Weibull-H family, Order statistics,
Parameter estimation, Simulation.
Determination of a probability distribution which should be adopted to make
inference about the data under study is a very important problem in statis-
tics. Because of this, considerable eﬀort over the years has been expended in
the development of large classes of distributions along with relevant statisti-
cal methodologies. In fact, the statistics literature is ﬁlled with hundreds of
continuous univariate distributions and their successful applications. There
has been a recent renewed interest in generating wider classes of distributions
by adding one (or more) shape parameter(s) to a baseline distribution, which
makes the generated distribution more ﬂexible, especially for studying tail
behavior. Modern computing technology has made many of these techniques
accessible even if analytical solutions are very complicated.
In the context of lifetime distributions with cumulative distribution
function (cdf) G(x), the most widely used generalization technique is the