On the Role of Extreme Summands in Sums of Independent Random Variables

Sums of independent identically distributed random variables are considered. It is assumed that the underlying distribution belongs to the domain of attraction of a stable law with the characteristic exponent $\alpha\in (0,1)\cup(1,2)$. We focus our attention on the limit distribution of those sums from which k extreme right and m extreme left summands are removed.

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