We explore some properties of the conditional distribution of an independently and identically distributed (i.i.d.) sample under large exceedances of its sum. Thresholds for the asymptotic independence of the summands are observed, in contrast with the classical case when the conditioning event is in the range of a large deviation. This paper is an extension of Broniatowski and Cao Extremes, 17 (2014), pp. 305-336. Tools include a new Edgeworth expansion adapted to specific triangular arrays, where the rows are generated by tilted distribution with diverging parameters, and some Abelian type results.
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机译：我们探讨了独立和相同分布 （i.i.d.） 样本在大超过其总和时的条件分布的一些性质。观察到求和的渐近独立性的阈值，这与条件事件在较大偏差范围内的经典情况形成鲜明对比。本文是 Broniatowski 和 Cao [Extremes， 17 （2014）， pp. 305-336] 的延伸。工具包括适用于特定三角形阵列的新 Edgeworth 展开，其中行是通过具有不同参数的倾斜分布生成的，以及一些阿贝尔类型结果。
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