  In this paper, we propose a reduced version of the new modified Weibull (NMW)
distribution due to Almalki and Yuan \cite{meNMW} in order to avoid some
estimation problems. The number of parameters in the NMW distribution is five.
The number of parameters in the reduced version is three. We study mathematical
properties as well as maximum likelihood estimation of the reduced version.
Four real data sets (two of them complete and the other two censored) are used
to compare the flexibility of the reduced version versus the NMW distribution.
It is shown that the reduced version has the same desirable properties of the
NMW distribution in spite of having two less parameters. The NMW distribution
did not provide a significantly better fit than the reduced version for any of
the four data sets.
