• 대한수학회보
• /
• 제45권3호
• /
• pp.509-522
• /
• 2008

The main aim of this paper is to present some results related to asymptotic behavior of distribution functions of random variables of chi-square type $X^2_N={\Sigma}^N_{i=1}\;X^2_i$ with degrees of freedom N, where N is a positive integer-valued random variable independent on all standard normally distributed random variables $X_i$. Two ways for computing the distribution functions of chi-square type random variables with random degrees of freedom are considered. Moreover, some tables concerning considered distribution functions are demonstrated in Appendix.

• Korean Journal of Mathematics
• /
• 제16권4호
• /
• pp.573-581
• /
• 2008

We obtain an improvement of strong laws of large numbers for independent fuzzy random variables.

• 한국지능시스템학회:학술대회논문집
• /
• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
• /
• pp.696-700
• /
• 1998

Fuzzy random variables with piecewise linear membership functions are introduced from a practical viewpoint. The estimation of the expected values of these fuzzy random variables is also discussed and statistical application is denonstratied by using a real data set.

• 충청수학회지
• /
• 제33권1호
• /
• pp.133-146
• /
• 2020

In this paper, we established the complete moment convergence for sequences of m-pairwise negatively quadrant dependent random variables which are weakly upper bounded by a random variable X.

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

• 대한수학회논문집
• /
• 제33권2호
• /
• pp.605-618
• /
• 2018

The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.

• 한국지능시스템학회논문지
• /
• 제15권1호
• /
• pp.98-103
• /
• 2005

본 논문에서는 구간수치 확률변수와 퍼지수치 확률변수를 생각하고 이들의 쇼케이 적분을 조사한다. 이러한 성질들을 이용하여 퍼지수치 확률변수의 르베그적분의 일반화인 퍼지수치 확률변수의 쇼케이 기대값을 정의한다. 특히 이들의 응용에 관한 예제들을 다룬다.

• 호남수학학술지
• /
• 제9권1호
• /
• pp.113-119
• /
• 1987

Random variables $X_1$, $X_1$, ..., $X_m$ are said to be weakly associated if whenever $\pi$ is a permutation of {1, 2,..., m}, $1{\leq}k<m$, and f: $R^{k}{\rightarrow}R$, g: $R^{m-k}{\rightarrow}R$ are coordinatewise nondecreasing functions then Cov $[f(X_{x(1)},...,\;X_{\pi(k)},\;g(X_{x(k+1)},...,\;X_{x(m)})]{\geq}0$, whenever the covariance is defined. An infinite collection of random variables is weakly associated if every finite subcollection is weakly associated. The basic properties of weak association and central limit theorem for weakly associated random variables are derived. We also extend this idea to point random fields and prove that a Cox process with a stationary weakly associated intensity rardom measure is weakly associated. Another inequalities and the fact that positive correlated normal random variables are weakly associated are also proved.

• 대한수학회지
• /
• 제54권3호
• /
• pp.877-896
• /
• 2017

In this paper, the complete convergence and complete moment convergence for a class of random variables satisfying the Rosenthal type inequality are investigated. The sufficient and necessary conditions for the complete convergence and complete moment convergence are provided. As applications, the Baum-Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for a class of random variables satisfying the Rosenthal type inequality are established. The results obtained in the paper extend the corresponding ones for some dependent random variables.

• 한국전산응용수학회:학술대회논문집
• /
• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
• /
• pp.8.2-8
• /
• 2003

The theory of fuzzy random variables and fuzzy stochastic processes has been received much attentions in recent years. But convergence in distribution for fuzzy random variables has not established yet. In this talk, we restrict our concerns to level-wise continuous fuzzy random variables and obtain some characterizations of its tightness and convergence in distribution.