• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.215-220
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• 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$^{p}$.

• 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.41 no.2
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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.

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

• Korean Journal of Mathematics
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• v.21 no.4
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• pp.383-399
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• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• Communications for Statistical Applications and Methods
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• v.10 no.1
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• pp.233-237
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• 2003

An asymptotic property of the ordinary least squares estimator of the disturbance variance is considered in the regression model with correlated errors. It is shown that the convergence in probability of S$^2$ is equivalent to the asymptotic unbiasedness. Beyond the assumption on the design matrix or the variance-covariance matrix of disturbances error, the result is quite general and simplify the earlier results.

• Proceedings of the Korean Reliability Society Conference
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• 2004.07a
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• pp.177-182
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• 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 $R^{p}$.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.3
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• pp.215-223
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• 2013

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 normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.427-440
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• 2024

The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t - M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.