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In this paper, a new family of distributions, called the Kumaraswamy odd log-logistic, is proposed and studied. Some mathematical properties are presented and special models are discussed. The asymptotes and shapes are investigated. The family density function is given by a linear combination of exponentiated densities following the same baseline model. We derive a power series for the quantile function, explicit expressions for the moments, quantile and generating functions and order statistics. We provide a bivariate extension of the new family. Its performance is illustrated by means of two real data sets.

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Bayesian inference, Beta function, Conjugate prior, Gamma distribution, Jefferys prior, Pivotal quantity,

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