On large deviations and density functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1979 English Publisher:Springer Science and Business Media LLCJournal:Annals of the Institute of Statistical Mathematics, volume 31, pages 315-317 (issn: 0020-3157, eissn: 1572-9052,

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Authors: Killeen, Timothy J.;

doi: 10.1007/bf02480288

On large deviations and density functions

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Abstract

Suppose thatX1,X2, ... is a sequence of absolutely continuous or integer valued random variables with corresponding probability density functionsfn(x). Let {φn} =1 ∞ be a sequence of real numbers, then necessary and sufficient conditions are given forn−1 logfn(φn)-n−1 log P (Xn>φn)=0(1) asn→∞.

Related Organizations

University of Connecticut
United States

Keywords

Large deviations, exponential rate, density behaviour

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