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. (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).
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Acknowledgements
We thank Prof. Gao for some discussion on Theorem 4.8 in Gao and Zhao (2011).
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CC and ML are supported by Indam-GNAMPA and by MIUR-PRIN 2017 Project ”Stochastic Models for Complex Systems” (No. 2017JFFHSH). CM and BP are supported by MIUR Excellence Department Project awarded to the Department of Mathematics, University of Rome Tor Vergata (CUP E83C18000100006), by University of Rome Tor Vergata (research program ”Beyond Borders”, project ”Asymptotic Methods in Probability” (CUP E89C20000680005)) and by Indam-GNAMPA (research project ”Stime asintotiche: principi di invarianza e grandi deviazioni”).
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Calì, C., Longobardi, M., Macci, C. et al. Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables. Metrika 85, 733–752 (2022). https://doi.org/10.1007/s00184-021-00849-8
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DOI: https://doi.org/10.1007/s00184-021-00849-8