• Bulletin of the Korean Mathematical Society
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• v.57 no.5
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• pp.1115-1126
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• 2020

The main purpose of this paper is to establish the rates of convergence in weak limit theorems for normalized geometric sums of independent identically distributed random variables via Zolotarev's probability metric.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.511-526
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• 2002

In this paper, we concern with SLLN for sums Of in-dependent random upper-semicontinuous fuzzy sets. We first give a generalization of SLLN for sums of independent and level-wise identically distributed random fuzzy sets, and establish a SLLN for sums of random fuzzy sets which is independent and compactly uniformly integrable in the strong sense. As a result, a SLLN for sums of independent and strongly tight random fuzzy sets is obtained.

• Bulletin of the Korean Mathematical Society
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• v.33 no.3
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• pp.419-425
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• 1996

Let ${X, X_n, n \geq 1}$ be a sequence of independent and identically distributed(i.i.d) random variables with EX = 0 and $E$\mid$X$\mid$^p < \infty$ for some $p \geq 1$. Let ${a_{ni}, 1 \leq i \leq n, n \geq 1}$ be a triangular arrary of constants. The almost sure(a.s) convergence of weighted sums $\sum_{i=1}^{n} a_{ni}X_i$ can be founded in Choi and Sung[1], Chow[2], Chow and Lai[3], Li et al. [4], Stout[6], Sung[8], Teicher[9], and Thrum[10].

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.37-49
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• 1999

We derive the almost sure convergence for weighted sums of random variables which are either pairwise positive quadrant dependent or pairwise positive quadrant dependent or pairwise negative quadrant dependent and then apply this result to obtain the almost sure convergence of weighted averages. e also extend some results on the strong law of large numbers for pairwise independent identically distributed random variables established in Petrov to the weighted sums of pairwise negative quadrant dependent random variables.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.255-258
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• 1997

We prove a conjecture of Yu. V. Prokhorov in general Banach Spaces ; let ($X_n$, n$\geq$1} be a sequence of independent identically and symmetrically distributed Banach valued random variables, then the relation $\mid$$\mid$$S_n$$\mid$$\mid$/$b_n$ -> 1 a.s. cannot hold for any choice of constants $b_n$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.385-388
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• 2004

The present paper establish the improved version of central limit theorem for sums of level-continuous fuzzy random variables as a generalization of central limit theorem for sums of independent and identically distributed random sets.

• Proceedings of the IEEK Conference
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• 2008.06a
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• pp.213-214
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• 2008

In this paper, we analyze the performance of a cooperative communication wireless network over independent and identically distributed (IID) Nakagami-m fading channels. A simple transmission scheme is considered where the relay is operating in amplify-forward (AF) mode. A closed-form expression for symbol error rate (SER) is obtained using the moment generating function (MGF) of the total signal to noise ratio (SNR) of the transmitted signal with binary phase shift keying (BPSK).

• Honam Mathematical Journal
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• v.34 no.2
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• pp.209-217
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• 2012

Convergence rates in the law of large numbers for i.i.d. random variables have been generalized by Gut[Gut, A., 1978. Marc inkiewicz laws and convergence rates in the law of large numbers for random variables with multidimensional indices, Ann. Probab. 6, 469-482] to random fields with all indices having the same power in the normalization. In this paper we generalize these convergence rates to the identically distributed and negatively associated random fields with different indices having different power in the normalization.

• The Journal of Korean Medical History
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• v.14 no.1
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• pp.79-108
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• 2001

Pyunjak is presumed to be Jinwallin who was active in early Chunchu period among five identically called doctors from early Chunchu period to Warring period. The name, Pyunjak, seems to be used as "special local doctor who goes around the country". This reflects the social atmosphere of the time that medical science and art were getting developed from royal household and government centered medicine to civilian-centered medicine.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.149-153
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• 2009

Let {$X_{n},\;n\;\geq\;1$} be a sequence of independent and identically distributed random variables with absolutely continuous cumulative distribution function (cdf) F(x) and probability density function (pdf) f(x). Suppose $X_{U(m)},\;m = 1,\;2,\;{\cdots}$ be the upper record values of {$X_{n},\;n\;\geq\;1$}. It is shown that the linearity of the conditional expectation of $X_{U(n+2)}$ given $X_{U(n)}$ characterizes the lomax, exponential and pareto distributions.