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Abstract
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We study general mathematical properties of a new generator of continuous
distributions with three extra shape parameters called the beta Marshall-Olkin family.
We present some special models and investigate the asymptotes and shapes. The new
density function can be expressed as a mixture of exponentiated densities based on
the same baseline distribution. We derive a power series for its quantile function.
Explicit expressions for the ordinary and incomplete moments, quantile and generating
functions, Bonferroni and Lorenz curves, Shannon and Rényi entropies and order
statistics, which hold for any baseline model, are determined. We discuss the
estimation of the model parameters by maximum likelihood and illustrate the flexibility
of the family by means of two applications to real data
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