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On large deviations and density functions

  • Timothy J. Killeen
Article
  • 13 Downloads

Abstract

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

A.M.S. 1970 subject classification

primary 6216 secondary 6030 

Key words and phrases

large deviation density 

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References

  1. [1]
    Killeen, T., Hettmansperger, T. and Sievers, G. (1972). An elementary theorem on the probability of large deviations,Ann. Math. Statist.,43, 181–192.MathSciNetCrossRefGoogle Scholar

Copyright information

© The Institute of Statistical Mathematics, Tokyo 1979

Authors and Affiliations

  • Timothy J. Killeen
    • 1
  1. 1.The University of ConnecticutConnecticutUSA

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