Sums of Independent Random Variables

  • Lucien Le Cam
Part of the Springer Series in Statistics book series (SSS)


This chapter collects a few facts, of the central limit theorem type, about distributions of sums of independent random variables.

Some of these facts will be used in Chapters 16 and 17 to study the distributions of logarithms of likelihood ratios in product experiments. However, these logarithms behave in a special manner which makes their study simpler than the general case considered here. The general classical central limit theorem can be obtained by a combination of three rather simple propositions.


Probability Measure Independent Random Variable Radon Measure Approximation Theorem Double Sequence 
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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Lucien Le Cam
    • 1
  1. 1.Department of StatisticsUniversity of CaliforniaBerkeleyUSA

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