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The Kumaraswamy distribution has been proposed as an alternative to the betadistribution with more benign algebraic properties. They have the same twoparameters, the same support and qualitatively similar shape for any parametervalues. There is a generic relationship between the distributions establishedby a simple transformation between arbitrary Kumaraswamy-distributed randomvariables and certain beta-distributed random variables. Here, a differentrelationship is established by means of the logistic map, the paradigmaticexample of a discrete non-linear dynamical system.

Kumaraswamy and beta distribution are related by the logistic map