DISCUSSION of “Models for extremes using the extended three-parameter Burr XII system with application to flood frequency analysis”* On the extended Burr XII distribution

The recent paper by Shao et al (2004) claims to have introduced a new model for frequency analysis referred to as the extended Burr XII distribution. The cumulative distribution function (cdf) and the probability density function (pdf) of this new distribution are specified as: { } { }      λ − − λ − − = c k c x x k x F) / (exp 1) / (1 1) (/ 1 0 if 0 if = ≠ k k (1) and { } { }      λ − λ λ λ − λ λ = − − − − − c c k c c x x c x k x c x f) / (exp) / () / (1) / () (1 1 1 / 1 1 1 0 if 0 if = ≠ k k (2) respectively, for 0 ≤ x < ∞ (if k ≤ 0), 0 ≤x ≤ λk-1/k (if k > 0), λ > 0 and c > 0. Shao et al. (2004) derive various properties of the distribution—including its moments, quantiles, and estimation procedure by the method of maximum likelihood—and provide an application to data from China. Unfortunately, the distribution given by equations (1) and (2) is by no means new. The same must be said of all of the properties of equations (1) and (2) that Shao et al. (2004) claim to have derived. The distribution given by equations (1) and (2) is the generalized Weibull distribution introduced by Mudholkar et al. (1996). The paper by Mudholkar et al. (1996) provides a comprehensive statistical treatment of the distribution with application to survival data. For related distributions and extensions, we refer See also the recent book by Murthy et al. (2004). The purpose of this correspondence is not just to point out the shortcomings of the paper by Shao et al. (2004). We feel the references mentioned above can help the