Weibull Distribution

This chapter describes two enhanced versions of Weibull distribution. These are Nukiyama-Tanasawa distribution, and q-Weibull distribution. The Nukiyama-Tanasawa distribution is an extension of the Weibull-II distribution. Employing a method similar to that used to develop the q-Gaussian distribution from the normal distribution, the q-Weibull distribution is developed from the Weibull distribution. It is another in the family of Tsallis distributions. If q is set to 1, the distribution reverts to the Weibull-II distribution. The chapter shows the effect of adjusting q. Using the stock level example, the chapter also hows that q-Weibull fits the data much better than Weibull. The parameter q is fitted as -2.75, with δ as 2.10 and β as 3802. As an example, the Weibull distribution predicts the probability of the stock level falling below 300 tonnes is 0.8%, equivalent to three occasions per year. The q-Weibull puts it much higher at 2.3%, or eight occasions per year.