A New Generalized Kumaraswamy Distribution
Authors: Jalmar M.F. Carrasco, Silvia L.P. Ferrari, Gauss M. Cordeiro
(Submitted on 6 Apr 2010)

Abstract: A new five-parameter continuous distribution which generalizes the Kumaraswamy and the beta distributions as well as some other well-known distributions is proposed and studied. The model has as special cases new four- and three-parameter distributions on the standard unit interval. Moments, mean deviations, R\’enyi’s entropy and the moments of order statistics are obtained for the new generalized Kumaraswamy distribution. The score function is given and estimation is performed by maximum likelihood. Hypothesis testing is also discussed. A data set is used to illustrate an application of the proposed distribution.

http://arxiv.org/abs/1004.0911v1

Ponnu

Try for your first example betaA=betaB=0.5 , K(a,b) = [4.3604471e-01 5.1398941e-01] and for the second example K(a,b) = [3.7355497e+00 3.4185949e+00]. Your page here made me work on this; the results are a couple of hours of work and hence need to be checked!

You can see my web page (software section) for other parameters, a full file of over 800 combinations.

Ponnu

But ever the optimist, I thought I could do better on choosing parameters. I realized around 1:30 AM it was not optimism but foolishness on my part. I thought I could do some fitting and come up with an empirical equation for estimating parameters. I was wrong!