Comparison of location models of Weibull type samples and extreme value processes (Q1092543)

Four different location parameter models are compared within the sufficiency and deficiency concept. The starting is a location model of a Weibull type sample with shape parameter \(-1<a<1\). Here our basic inequality concerns the approximate sufficiency of the k lower extremes. In addition, the lower extremes are approximately equal, in distribution, to \((S_ m^{1/(1+a)}+t)_{m\leq k}\) where \(S_ m\) is the sum of m i.i.d. standard exponential random variables and t is the location parameter. The final step leads us to the model of extreme value processes \((S_ m^{1/(1+a)}+t)_{m=1,2,3,...}\).