On the moments of the modified Weibull distribution

In a recent paper, Xie et al. [Reliab Eng Syst Saf 2002;76:279–85] proposed a modification of the Weibull distribution to allow it to exhibit bathtub-shaped failure rate functions. In this note, we derive explicit algebraic formulas for the kth moment of the distribution. The formulas allow one to calculate the moments for a wide range of values of k and the shape parameter of the modified Weibull. They also allow one to calculate the moments more easily with less computational time. Besides being of interest in their own, we believe that these formulas will be useful for any follow-up mathematical study of the proposed distribution.