The paper by Rao and Kakehashi 
uses the Weibull distribution (given by equation (3) in the paper)
and a truncated version of it (given by equations (4) and (5))
to model HIV/AIDS data in India.
After a careful reading, I have found that all of the results presented
in the appendix are incorrect (starting with equation (11) itself).
Instead of pointing out all of the specific errors, I have chosen to give the
correct formulas (and a brief outline of their derivation)
for the $r$th moment of the truncated Weibull distribution.