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1 results

  • Saddle point approximation for the distribution of the sum of independent random variables

  • Robert Lugannani, Stephen Rice
  • Journal:
    Advances in Applied Probability / Volume 12 / Issue 2 / June 1980
    Published online by Cambridge University Press:
    01 July 2016, pp. 475-490
    Print publication:
    June 1980
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  • In the present paper a uniform asymptotic series is derived for the probability distribution of the sum of a large number of independent random variables. In contrast to the usual Edgeworth-type series, the uniform series gives good accuracy throughout its entire domain. Our derivation uses the fact that the major components of the distribution are determined by a saddle point and a singularity at the origin. The analogous series for the probability density, due to Daniels, depends only on the saddle point. Two illustrative examples are presented that show excellent agreement with the exact distributions.