• Journal of the Korean Institute of Intelligent Systems
• /
• v.14 no.7
• /
• pp.852-856
• /
• 2004

The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

• Communications for Statistical Applications and Methods
• /
• v.19 no.5
• /
• pp.647-654
• /
• 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.

• Proceedings of the Korean Reliability Society Conference
• /
• 2004.07a
• /
• pp.177-182
• /
• 2004

In this paper, we establish some results on almost sure convergence for sums and weighted sums of uniformly integrable fuzzy random sets taking values in the space of upper-semicontinuous fuzzy sets in $R^{p}$.

• Journal of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.327-349
• /
• 2021

In this paper, we main study the strong law of large numbers and complete convergence for weighted sums of asymptotically almost negatively associated (AANA, in short) random variables, by using the Marcinkiewicz-Zygmund type moment inequality and Roenthal type moment inequality for AANA random variables. As an application, the complete consistency for the weighted linear estimator of nonparametric regression models based on AANA errors is obtained. Finally, some numerical simulations are carried out to verify the validity of our theoretical result.

• Communications for Statistical Applications and Methods
• /
• v.16 no.3
• /
• pp.529-540
• /
• 2009

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of fuzzy numbers of the real line R. We first give improvements of WLLN for weighted sums of convex-compactly uniformly integrable fuzzy random variables obtained by Joo and Hyun (2005). And then, we consider the case that the averages of expectations of fuzzy random variables converges. As results, WLLN for weighted sums of convexly tight or identically distributed case is obtained.

• Journal of the Korean Mathematical Society
• /
• v.53 no.1
• /
• pp.45-55
• /
• 2016

Let {$X_n,n{\geq}1$} be a sequence of negatively superadditive dependent random variables. In the paper, we study the strong law of large numbers for general weighted sums ${\frac{1}{g(n)}}{\sum_{i=1}^{n}}{\frac{X_i}{h(i)}}$ of negatively superadditive dependent random variables with non-identical distribution. Some sufficient conditions for the strong law of large numbers are provided. As applications, the Kolmogorov strong law of large numbers and Marcinkiewicz-Zygmund strong law of large numbers for negatively superadditive dependent random variables are obtained. Our results generalize the corresponding ones for independent random variables and negatively associated random variables.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.209-213
• /
• 2002

We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

• Honam Mathematical Journal
• /
• v.26 no.3
• /
• pp.287-298
• /
• 2004

In this paper we derive complete convergences for weighted sums of asymptotically almost negatively associated random variables.

• Journal of the Korean Mathematical Society
• /
• v.42 no.5
• /
• pp.949-957
• /
• 2005

For weighted sum of a sequence {X, X$\_{n}$, n $\geq$ 1} of identically distributed, negatively orthant dependent random variables such that |r| > 0, has a finite moment generating function, a strong law of large numbers is established.

• Proceedings of the Korean Statistical Society Conference
• /
• 2002.11a
• /
• pp.215-220
• /
• 2002

In this paper, we establish weak laws of large numbers for weighted sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.