• Journal of the Chungcheong Mathematical Society
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• v.25 no.1
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• pp.97-103
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• 2012

In this paper, we introduce the notion of the statist-cally fuzzy convergent sequence and the statistical fuzzy ${\alpha}$-Cauchy sequence of fuzzy points in a fuzzy normed linear space. And investigate some related properties.

• Journal of applied mathematics & informatics
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• v.40 no.1_2
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• Bulletin of the Korean Mathematical Society
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• v.47 no.4
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• pp.825-837
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• 2010

In this paper, we obtain a Korovkin type approximation theorem for double sequences of positive linear operators of two variables from $H_w$ (K) to C (K) via A-statistical convergence. Also, we construct an example such that our new approximation result works but its classical case does not work. Furthermore, we study the rates of A-statistical convergence by means of the modulus of continuity.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.203-211
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• 2003

A new result of weak convergence of the empirical process is established for a stationary ${\phi}-mixing$ sequence of random variables, which relaxes the existing conditions on mixing coefficients. The result is basically obtained from bounds for even moments of sums of ${\phi}-mixing$ r.v.'s useful for handling triangular arrays with entries decreasing in size.

• Journal of the Korean Statistical Society
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• v.28 no.4
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• pp.435-441
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• 1999

A 'convergence in probability' rate of the empirical distributions and quantiles of linear processes is obtained. As an application of the limit theorems, a trimmed mean for the location of the linear process is considered. It is shown that the trimmed mean is asymptotically normal. A consistent estimator for the asymptotic variance of the trimmed mean is provided.

• Journal of the Korean Statistical Society
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• v.31 no.1
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• pp.33-43
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• 2002

The empirical Bayes linear loss two-action problem is studied. An empirical Bayes test $\delta$$_{n}$ $^{*}$ is proposed. It is shown that $\delta$$_{n}$ $^{*}$ is asymptotically optimal in the sense that its regret converges to zero at a rate $n^{-1}$ over a class of priors and the rate $n^{-1}$ is the optimal rate of convergence of empirical Bayes tests.sts.

• Tunnel and Underground Space
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• v.13 no.2
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• pp.108-116
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• 2003

Measured convergence data of a tunnel were investigated by means of statistical and regression analysis, where the rock mass were mainly composed of andesite and granite. The rock mass around tunnel were classified by RMR method into five different ratings, and then convergence data which belong to individual ratings were statistically processed to find out the appropriate regression equations. Exponential equations were better coincided with measured data than logarithmic equations. As the number of rock mass rating was increased, the magnitude and standard deviation of convergence were increased. Final convergence data were also investigated to study the relevance with both maximum displacement rate and early measured convergence. Some brief results of their relevance are presented. For instance, the regression coefficient between final convergence and maximum displacement rate was turned out to be 0.87 for this studied tunnel.

• Journal of the Korean Statistical Society
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• v.31 no.2
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• pp.261-276
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• 2002

Probability density or its derivatives may have a discontinuity/change point at an unknown location. We propose a method of estimating the location and the jump size of the discontinuity point based on kernel type density or density derivatives estimators with one-sided equivalent kernels. The rates of convergence of the proposed estimators are derived, and the finite-sample performances of the methods are illustrated by simulated examples.

• Proceedings of the Korean Geotechical Society Conference
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• 1993.03a
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• pp.27-32
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• 1993

In tunnelling by NATM convergence data are most Importantly to ascertain the safety of tunnel. Therefore, a reliable method is required that can predict ultimate displacements by using earler displacement data. Displacement forecasting method is classified into statistical method and functional regression method. Convergence data measured in Seoul subway 5~45 site during '92.5 ~ '92.12 were analyzed by above said two methods. The analysis results of convergence data show that the functional regression method is more relieable in completely weathered rock, but the statistical method in slightly wearhred rock.

• Communications for Statistical Applications and Methods
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• v.12 no.2
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• pp.275-283
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• 2005

In this paper, we give a sufficient condition for convergence in probability of weighted sums of convex-compactly uniformly integrable fuzzy random variables. As a result, we obtain weak law of large numbers for weighted sums of convexly tight fuzzy random variables.