Journal of the Korean Data and Information Science Society

  • Volume 4
  • /
  • Pages.53-63
  • /
  • 1993
  • /
  • 1598-9402(pISSN)
The Korean Data and Information Science Society (한국데이터정보과학회)
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On the Weak Law of Large Numbers for the Sums of Sign-Invariant Random Variables

대칭확률변수(對稱確率變數)의 대수(對數)의 법칙(法則)에 대하여

  • Hong, Dug-Hun (Department of Statistics, Hyosung Women's National University)
  • Published : 1993.06.25
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Abstract

We consider various types of weak convergence for sums of sign-invariant random variables. Some results show a similarity between independence and sign-invariance. As a special case, we obtain a result which strengthens a weak law proved by Rosalsky and Teicher [6] in that some assumptions are deleted.

Keywords

References

  1. Real analysis and Probability Ash, R.B.
  2. Ann. Math. Statist. v.33 An extension of the arc sine law Berman, S.M.
  3. Trans. Amer. Math. Soc. v.119 Sign-invariant random variables and stochastic processes with sign-invariant increments Berman, S.M.
  4. Probability theory : independence, interchangeability, martingales Chow, Y.S.;Teicher, H.
  5. Proc. Cambridge. Phil. Soc. v.69 Convergence of weighted sums of independent random variables Rohatgi, V.K.
  6. Ann. Math. Probability v.9 A limit theorem for double arrays Rosalsky, A.J.;Teicher, H.