We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous functions defined on [0, 1] which satisfy some suitable conditions. In this way we generalize some recent results by Giuliano et al. (2015) which concern the empirical cumulative entropies defined in Di Crescenzo and Longobardi (2009a).

中文翻译：

---

由iid指数随机变量生成的间距的线性组合的渐近结果

对于由iid指数分布的随机变量生成的一类间距的线性组合，我们证明了较大（中等）偏差。我们允许一类广泛的系数，这些系数可以用满足一些合适条件的[0，1]上定义的连续函数来表示。这样，我们概括了Giuliano等人的一些最新结果。（2015年）涉及Di Crescenzo和Longobardi（2009a）中定义的经验累积熵。