The two-parameter Weibull distribution is a very popular distribution
that has been extensively used over the past decades
for modeling data in reliability, engineering and biological
studies. It is well-known that the major weakness of the Weibull
distribution is its inability to accommodate nonmonotone
failure rates. The first generalization of the two-parameter
Weibull distribution to accommodate nonmonotone failure
rates was introduced by [1] and it is known as the exponentiated
Weibull (EW) distribution. The three-parameter EW distribution
has cumulative function in the form