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).

翻译：我们证明,对于由i.d.指数分布式随机变量生成的一组间距的线性组合,存在着很大的(和中度的)偏差。我们允许一系列广泛的系数,可以用[0,1]确定的持续功能表示,这些功能符合某些适当条件。我们这样概括了朱利亚诺等人(2015年)最近的一些结果,这些结果涉及Di Crescenzo和Longobardi(2009年a)所界定的经验累积性离心动物。