Comparison of location models of Weibull type samples and extreme value processes

Abstract

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 $$\left( {S_m^{1/(1 + a)} + t} \right)_{m \leqq k} $$ 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 $$\left( {S_m^{1/(1 + a)} + t} \right)_{m = 1,2,3} $$ ...