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There exist well-known necessary and sufficient conditions for a distribution function to belong to the domain of attraction of the double exponential distribution Λ. For practical purposes a simple sufficient condition due to von Mises is very useful. It is shown that each distribution function F in the domain of attraction of Λ is tail equivalent to some distribution function satisfying von Mises' condition.
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Balkema et al. (1972) studied this question.
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