• Communications for Statistical Applications and Methods
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• 제12권1호
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• pp.117-123
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• 2005

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.

• Journal of the Korean Data and Information Science Society
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• 제20권1호
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• pp.191-202
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• 2009

In this study, we drive the one dimensional marginal transform function, probability density function and probability distribution function for the random variables $T_{{\xi}N}$ (Time taken by the servers during the vacations), ${\xi}_N$(Number of vacations taken by the servers) and ${\eta}_N$(Number of customers or units arrive in the system) by controlling the variability of two random variables simultaneously.

• Journal of applied mathematics & informatics
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• 제4권1호
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• pp.211-222
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• 1997

In this paper we present a probabilistic approach for the estimation of realistic error bounds appearing in the execution of basic algebraic floating point operations. Experimental results are carried out for the extended product the extended sum the inner product of random normalised numbers the product of random normalised ma-trices and the solution of lower triangular systems The ordinary and probabilistic bounds are calculated for all the above processes and gen-erally in all the executed examples the probabilistic bounds are much more realistic.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.99-103
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• 2003

In this note we find the exact Probability distribution of d$\_$n, i/ the outdegree of the node i, in a random recursive tree with n nodes. For i = i$\_$n/ increasing as a linear function on n, we show that d$\_$n/,i$\_$n/ is asymptotically normal.

• Journal of applied mathematics & informatics
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• 제27권3_4호
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• pp.885-893
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• 2009

In this paper we study the strong law of large numbers for weighted average of pairwise negatively quadrant dependent random variables. This result extends that of Jamison et al.(Convergence of weight averages of independent random variables Z. Wahrsch. Verw Gebiete(1965) 4 40-44) to the negative quadrant dependence.

• Journal of the Korean Statistical Society
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• 제28권1호
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• pp.21-34
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• 1999

In this paper, conditional expectation of a fuzzy random variable is introduced and its properties are investigated. Using this, we introduce the concept of fuzzy martingales and prove some convergence theorems which generalize te corresponding results for the classical martingales.

• Journal of the Korean Statistical Society
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• 제34권1호
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• pp.1-9
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• 2005

In this paper we establish the Hajeck-Renyi type inequality for asymptotically quadrant sub-independent random variables and derive the strong law of large numbers by this inequality.

• 대한수학회지
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• 제53권6호
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• pp.1275-1292
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• 2016

The Marcinkiewicz-Zygmund strong law of large numbers for conditionally independent and conditionally identically distributed random variables is an existing, but merely qualitative result. In this paper, for the more general cases where the conditional order of moment belongs to (0, ${\infty}$) instead of (0, 2), we derive results on convergence rates which are quantitative ones in the sense that they tell us how fast convergence is obtained. Furthermore, some conditional probability inequalities are of independent interest.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 2007년도 춘계종합학술대회
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• pp.803-806
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• 2007

TRNG (True Random Number Generator)를 테스트 하는 방법은 PRNG (Pseudo Random Number Generator)나 산술연산기를 비롯한 결정적 (deterministic) 소자에 대한 테스트와는 많이 틀려서, 새로운 개념과 방법론이 제시되어야 한다. 하드웨어적으로 결정적인 소자들은 패턴을 사용한 테스트 (ATPG; automatic test pattern generation)에 의해 커버가 될 수 있지만, 순수 난수는 발생 결과의 아날로그적인 특성에 의하여 자동 패턴 생성 방식에 의해 소자를 테스트하기가 불가능하다. 본 논문에서는 하드웨어와 소프트웨어를 결합한 테스트 방식으로 테스트 패턴에 연속적인 패턴의 변화를 주면서 통계적으로 관찰하는 방식인 Diehard test라는 테스트 방식을 연구, 분석하고, 순수 난수의 테스트 시 고려해야 할 주안점을 제안한다.

• Communications for Statistical Applications and Methods
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• 제18권6호
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• pp.799-808
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• 2011

Let {${\Omega}$, $\mathcal{F}$, P} be a probability space and {$X_n{\mid}n{\geq}1$} be a sequence of random variables defined on it. A finite sequence of random variables {$X_i{\mid}1{\leq}i{\leq}n$} is a conditional associated given $\mathcal{F}$ if for any coordinate-wise nondecreasing functions f and g defined on $R^n$, $Cov^{\mathcal{F}}$ (f($X_1$, ${\ldots}$, $X_n$), g($X_1$, ${\ldots}$, $X_n$)) ${\geq}$ 0 a.s. whenever the conditional covariance exists. We obtain the H$\grave{a}$jek-R$\grave{e}$nyi-type inequality for conditional associated random variables. In addition, we establish the strong law of large numbers, the three series theorem, integrability of supremum, and a strong growth rate for $\mathcal{F}$-associated random variables.