• Title/Summary/Keyword: Sign-invariant random variables

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On the Law of the Iterated Logarithm without Assumptions about the Existence of Moments for the Sums of Sign-Invariant Random Variables (부호불변(符號不變) 확률변수(確率變數)에 합(合)에 대한 반복대수(反復對數)의 법칙(法則))

  • Hong, Dug-Hun
    • Journal of the Korean Data and Information Science Society
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    • v.2
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    • pp.41-44
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    • 1991
  • Petrov (1968) gave two theorems on the law of the iterated logarithm without any assumptions about the existence of moments of independent random variables. In the present paper we show that the same holds true for sign-invariant random variables.

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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
    • Journal of the Korean Data and Information Science Society
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    • v.4
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    • pp.53-63
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    • 1993
  • 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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On a Stopping Rule for the Random Walks with Time Stationary Random Distribution Function

  • Hong, Dug-Hun;Oh, Kwang-Sik;Park, Hee-Joo
    • Journal of the Korean Statistical Society
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    • v.24 no.2
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    • pp.293-301
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    • 1995
  • Sums of independent random variables $S_n = X_1 + \cdots + X_n$ are considered, where the $X_n$ are chosen according to a stationary process of distributions. For $c > 0$, let $t_c$ be the smallest positive integer n such that $$\mid$S_n$\mid$ > cn^{\frac{1}{2}}$. In this set up we are concerned with finiteness of expectation of $t_c$ and we have some results of sign-invariant process as applications.

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