Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

  • Authors:

  • K. Nakagawa

  • Affiliations:

  • Nagaoka Univ. of Technol., Niigata

  • Venue:
  • IEEE Transactions on Information Theory
  • Year:
  • 2007

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Abstract

In this correspondence, we give a sufficient condition for the exponential decay of the tail probability of a nonnegative random variable. We consider the Laplace-Stieltjes transform of the probability distribution function of the random variable. We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail probability decays exponentially. For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.