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Extension of Edgeworth type expansion of the distribution of the sums of I.I.D. random variables in non-regular cases

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Abstract

The asymptotic expansions of the distributions of the sums of independent identically distributed random variables are given by Edgeworth type expansions when moments do not necessarily exist, but when the density can be approximated by rational functions.

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References

  1. Gnedenko, B. V. and Kolmogorov, A. N. (1954).Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Cambridge, Massachussets, (Translated from Russian).

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Authors and Affiliations

  1. University of Tokyo, Tokyo, Japan

    Kei Takeuchi & Masafumi Akahira

  2. University of Electro-Communications, Tokyo, Japan

    Kei Takeuchi & Masafumi Akahira

Authors
  1. Kei Takeuchi
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  2. Masafumi Akahira
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Supported in part by the Sakkokai Foundation.

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Takeuchi, K., Akahira, M. Extension of Edgeworth type expansion of the distribution of the sums of I.I.D. random variables in non-regular cases. Ann Inst Stat Math 29, 397–406 (1977). https://doi.org/10.1007/BF02532800

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  • DOI: https://doi.org/10.1007/BF02532800

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