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. (J Statist Plann Inference 157–158:77–89, 2015) which concern the empirical cumulative entropies defined in Di Crescenzo et al. (J Statist Plann Inference 139:4072–4087, 2009a).

中文翻译：

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由 iid 指数随机变量生成的间距线性组合的渐近结果

我们证明了由 iid 指数分布的随机变量生成的一类间距线性组合的大（和中等）偏差。我们允许大量的系数可以用定义在 [0, 1] 上的连续函数来表示，这些函数满足一些合适的条件。通过这种方式，我们概括了 Giuliano 等人最近的一些结果。（J Statist Plann Inference 157–158:77–89, 2015）涉及 Di Crescenzo 等人定义的经验累积熵。(J Statist Plann Inference 139:4072–4087, 2009a)。