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Abstract
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The proposal of more flexible distributions is an activity often required in practical con-
texts. In particular, adding a positive real parameter to a probability distribution by
exponentiation of its cumulative distribution function has provided flexible generated
distributions having interesting statistical properties. In this paper, we study general
mathematical properties of a new generator of continuous distributions with three extra
parameters called the exponentiated Gompertz generated (EGG) family. We present
some of its special models as well as an essay on its physical motivation. From math-
ematical point of view, we derive explicit expressions of the EGG family: the ordinary
and incomplete moments, quantile and generating functions, Bonferroni and Lorenz
curves, Shannon and Rényi entropies and order statistics, which are valid for any base-
line model. We also provide a bivariate EGG extension. The estimation procedure by
maximum likelihood of the new class is elaborated and discussed. In order to quantify
and to assess the asymptotic behavior of this procedure, we perform a simulation study.
Finally, two applications to real data are performed. Results furnish evidence in favor
of the use of the EGG beta distribution as a good proposal to these data sets.
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