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Asymptotic distributions of the generalized and the dual generalized extremal quotient. (English) Zbl 1272.62021

Summary: Necessary and sufficient conditions for the weak convergence of the generalized and the dual generalized extremal quotient are obtained. The class of possible nondegenerate limit distribution functions of quotient of generalized and its dual extreme order statistics is characterized. Some illustrative examples are obtained.

MSC:

62E20 Asymptotic distribution theory in statistics
62G32 Statistics of extreme values; tail inference
62G30 Order statistics; empirical distribution functions
60F05 Central limit and other weak theorems
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