• 대한수학회논문집
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• 제21권4호
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• pp.771-778
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• 2006

Strong laws are established for linear statistics that are weighted sums of a random sample. We show extensions of the Marcinkiewicz-Zygmund strong laws under certain moment conditions on both the weights and the distribution. The result obtained extends and sharpens the result of Sung ([12]).

• 대한수학회보
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• 제47권2호
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• pp.369-383
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• 2010

We obtain a result on complete convergence of weighted sums for arrays of rowwise independent Banach space valued random elements. No assumptions are given on the geometry of the underlying Banach space. The result generalizes the main results of Ahmed et al. [1], Chen et al. [2], and Volodin et al. [14].

• 대한수학회보
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• 제43권3호
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• pp.611-617
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• 2006

In this paper we construct q-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the q-analogue of alternating sums of powers of consecutive integers due to Euler.

• 대한수학회보
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• 제41권2호
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• pp.275-282
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• 2004

Let {$a_{ni},\;u_n\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be an arry of constants. Let {X_{ni},\;u_n\;{\leq}\;i\;{\leq}\;{\upsilon}_n,\;n\;{\geq}\;1$} be {$a_{ni}$}-uniformly integrable random variables. Weak laws for the weighted sums ${{\Sigma}_{i=u_n}}^{{\upsilon}_n}\;a_{ni}X_{ni}$ are obtained.

• 호남수학학술지
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• 제36권3호
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• pp.647-657
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• 2014

In this paper, we study combinatoric convolution sums of divisor functions and get values of this sum when $n=2^mp$. We find that the value of this convolution sum is represented by a sum of powers of 2 and Bernoulli or Euler number.

• 한국지능시스템학회논문지
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• 제14권7호
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• pp.852-856
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• 2004

이 논문에서는 퍼지 랜덤 변수의 합에 대한 약한 대수의 법칙을 일반화로서, 컴팩트 일양 적분 가능한 수준 연속 퍼지 랜덤 변수의 가중 합이 약 수렴하기 위한 동치 조건을 구하였다.

• 자연과학논문집
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• 제13권1호
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• pp.1-6
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• 2003

높은 차수의 적률을 갖는 i.i.d. 확률 변수의 가중합에 대한 강대수 법칙을 유도한다. 또한 Sung (2001)의 결과 중 하나를 확장한다.

• Communications for Statistical Applications and Methods
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• 제19권5호
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• pp.647-654
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• 2012

We discuss the strong convergence for weighted sums of linearly negative quadrant dependent(LNQD) random variables under suitable conditions and the central limit theorem for weighted sums of an LNQD case is also considered. In addition, we derive some corollaries in LNQD setting.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.407-415
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• 2011

We establish strong laws of large numbers for weighted sums of arrays of negatively associated random variables under the condition of h-integrability and suitable conditions on the array of weights.

• 대한수학회보
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• 제38권1호
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• pp.55-63
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• 2001

In this paper, we derive a general strong law of large numbers and a general weak law of large number for normed weighted sums of pairwise negative quadrant dependent random variables with the common distribution function.