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Abstract
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We introduce and study general mathematical properties of a new generator of continuous distributions with three extra parameters called
the extended Cordeiro and de Castro family. We investigate the asymptotes and shapes. The new density function can be expressed as a linear
combination of exponentiated densities based on the same underlying
distribution. We derive a power series for the quantile function of this
family. We determine explicit expressions for the ordinary and incomplete moments, quantile and generating functions, asymptotic distribution of the extreme values, Shannon and Rényi entropies and order
statistics, which hold for any baseline model. We discuss the estimation of the model parameters by maximum likelihood and illustrate the
potentiality of the introduced family by means of two applications to
real data.
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