Mitnik, Pablo. 2013. “New Properties of
the Kumaraswamy Distribution,” *Communications
and Statistics – Theory and Methods* 42(5):741-755.

**Abstract**

The
Kumaraswamy distribution is very similar to the Beta distribution but has the
key advantage of a closed-form cumulative distribution function. This makes it
much better suited than the Beta distribution for computation-intensive
activities like simulation modeling and the estimation of models by
simulation-based methods. However, in spite of the fact that the Kumaraswamy
distribution was introduced in 1980, further theoretical research on the
distribution was not developed until very recently (Garg, 2008; Jones, 2009;
Mitnik, 2009; Nadarajah, 2008). This article contributes to this recent
research and: (a) shows that Kumaraswamy variables exhibit closeness under
exponentiation and under linear transformation; (b) derives an expression for
the moments of the general form of the distribution; (c) specifies some of the
distribution's limiting distributions; and (d) introduces an analytical
expression for the mean absolute deviation around the median as a function of
the parameters of the distribution, and establishes some bounds for this
dispersion measure and for the variance.