Maximizing the entropy of a sum of independent bounded random variables

  • Authors:
  • E. Ordentlich

  • Affiliations:
  • Hewlett-Packard Labs., Palo Alto, CA

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2006

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Abstract

Let X1,...,Xn be n independent, symmetric random variables supported on the interval [-1,1] and let Sn=sigmai=1 nXi be their sum. We show that the differential entropy of Sn is maximized when X1,...,Xn-1 are Bernoulli taking on +1 or -1 with equal probability and Xn is uniformly distributed