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