Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables

TL;DR

This paper establishes large and moderate deviation principles for linear combinations of spacings from i.i.d. exponential variables, generalizing previous results to a broader class of coefficients expressed via continuous functions.

Contribution

It extends existing large deviation results to a wider class of linear combinations of spacings, incorporating more general coefficient functions.

Findings

Proves large deviation principles for linear combinations of spacings.

Generalizes previous results by Giuliano et al. (2015).

Includes moderate deviation results for the same class of statistics.

Abstract

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).