Summary
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 \(\left( {S_m^{1/(1 + a)} + t} \right)_{m = 1,2,3} \)...
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Janssen, A., Reiss, RD. Comparison of location models of Weibull type samples and extreme value processes. Probab. Th. Rel. Fields 78, 273–292 (1988). https://doi.org/10.1007/BF00322024
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DOI: https://doi.org/10.1007/BF00322024