Journal of the Korean Data and Information Science Society

  • 제4권
  • /
  • Pages.53-63
  • /
  • 1993
  • /
  • 1598-9402(pISSN)
한국데이터정보과학회 (The Korean Data and Information Science Society)
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대칭확률변수(對稱確率變數)의 대수(對數)의 법칙(法則)에 대하여

On the Weak Law of Large Numbers for the Sums of Sign-Invariant Random Variables

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

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.

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참고문헌

  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.