Skip to main content
SpringerLink
Log in

On the remained term for the central limit theorem

  • Published:
Annals of the Institute of Statistical Mathematics Aims and scope Submit manuscript

Summary

An upper bound for the remainder term of the Edgeworth expansion for the distribution of the normalized sum of independent and identically distributed random variables is given in terms of 3rd and 4th order moments, together with the total variation of the probability density function of the underlying distribution.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Refrences

  1. Feller, W. (1966).An Introduction to Probability Theory and its Applications II, John Wiley, New York.

    Google Scholar 

  2. Gnedenko, B. V. and Kolmogorov, A. N. (1967)Limit Distributions for Sum of Independent Random Variables (English translation), Addision-Wesley, Cambridge, Mass.

    Google Scholar 

  3. Rogozin, B. A. (1965). On the maximum of the density of the sum of random variables with unimodal distribution,Litovsk. Mat. Sb.,5, 499–503, English translation:Selected Transl. Math. Statist. and Prob.,9, 69–74, 1970.

    MATH  MathSciNet  Google Scholar 

Download references

Authors
  1. Ryoichi Shimizu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The Institute of Statistical mathematics

About this article

Cite this article

Shimizu, R. On the remained term for the central limit theorem. Ann Inst Stat Math 26, 195–201 (1974). https://doi.org/10.1007/BF02479815

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02479815

Keywords

Search

Navigation