The exponentiated Weibull family extends the two-parameter Weibull distribution. The shape of the Weibull plotting-paper plots are discussed, and a parametric characterization of the pdf and the failure rate for the exponentiated Weibull family are carried out. Such a study is very relevant to deciding if a given data set can be adequately modeled by such a distribution.
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Jiang et al. (1999) studied this question.