• Journal of the Korean Mathematical Society
• /
• v.32 no.1
• /
• pp.141-149
• /
• 1995

Let N denote the set of positive integers. Fix $d_1, d_2 \in N with d = d_1 + d_2$. Let X and Y be real random variables and let ${X_i : i \in N^d_1} and {Y_j : j \in N^d_2}$ be independent families of independent identically distributed random variables with $L(X) = L(X_i) and L(Y) = L(Y_j)$, where $L(\cdot)$ denote the law of $\cdot$.

• Journal of applied mathematics & informatics
• /
• v.30 no.3_4
• /
• pp.647-653
• /
• 2012

In this paper, we consider fuzzy random sets as (measurable) mappings from a probability space into the set of fuzzy sets and prove a uniform strong law of large numbers for sequences of independent and identically distributed fuzzy random sets. Our results generalize those of Bass and Pyke(1984)and Jang and Kwon(1998).

• Communications of the Korean Mathematical Society
• /
• v.20 no.3
• /
• pp.531-538
• /
• 2005

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.1
• /
• pp.127-136
• /
• 2010

For the maximum partial sum of linear process generated by a doubly infinite sequence of identically distributed $\rho$-mixing random variables with mean zeros, a complete convergence is obtained under suitable conditions.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.529-538
• /
• 2006

In this paper we derive the central limit theorem for ${\sum}^n_{i=l}\;a_{ni}{\xi}_{i},\;where\;\{a_{ni},\;1\;{\le}\;i\;{\le}n\}$ is a triangular array of non-negative numbers such that $sup_n{\sum}^n_{i=l}\;a^2_{ni}\;<\;{\infty},\;max_{1{\le}i{\le}n\;a_{ni}{\to}\;0\;as\;n{\to}{\infty}\;and\;{\xi}'_{i}s$ are a linearly positive quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process of the form $X_n\;=\;{\sum}^{\infty}_{j=-{\infty}}a_{k+j}{\xi}_{j}$.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
• /
• v.19 no.2
• /
• pp.162-168
• /
• 2006

Recently, diagnosis techniques have been investigated to detect a Partial Discharge associated with a dielectric material defect in a high voltage electrical apparatus, However, the properties of detection technique of Partial Discharge aren't completely understood because the physical process of Partial Discharge. Therefore, this paper analyzes the process on surface discharge of polymer insulator using wavelet transform. Wavelet transform provides a direct quantitative measure of spectral content in the time~frequency domain. As it is important to develop a non-contact method for detecting the kaolin contamination degree, this research analyzes the electromagnetic waves emitted from Partial Discharge using wavelet transform. This result experimentally shows the process of Partial Discharge as a two-dimensional distribution in the time-frequency domain. Feature extraction parameter namely, maximum and average of wavelet coefficients values, wavelet coefficients value at the point of $95\%$ in a histogram and number of maximum wavelet coefficient have used electromagnetic wave signals as input signals in the preprocessing process of neural networks in order to identify kaolin contamination rates. As result, root sum square error was produced by the test with a learning of neural networks obtained 0.00828.

• Communications for Statistical Applications and Methods
• /
• v.2 no.1
• /
• pp.194-200
• /
• 1995

The baker's transformation is an ergodic transformation defined on the half open unit square. This paper considers the limiting begavior of the partial sum process of a martingale sequence constructed from the baker's transformation in the context of an invariance principle of a uniform central limit theorm.

• Bulletin of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.617-626
• /
• 2009

Let {$Y_i$,-$\infty$ < i < $\infty$} be a doubly infinite sequence of i.i.d. random variables with E|$Y_1$| < $\infty$, {$a_{ni}$,-$\infty$ < i < $\infty$ n $\geq$ 1} an array of real numbers. Under some conditions on {$a_{ni}$}, we obtain necessary and sufficient conditions for $\sum\;_{n=1}^{\infty}\frac{1}{n}P(|\sum\;_{i=-\infty}^{\infty}a_{ni}(Y_i-EY_i)|$>$n{\epsilon})$<{\infty}$. We examine whether the result of Spitzer [11] holds for the moving average process, and give a partial solution.

• Journal of the Korean Data and Information Science Society
• /
• v.21 no.5
• /
• pp.901-908
• /
• 2010

A geometrical description method is proposed to represent the process of the forward selection and backward elimination methods among many variable selection methods for multiple regression models. This graphical method shows the process of the forward selection and backward elimination on the first and second quadrants, respectively, of half circle with a unit radius. At each step, the SSR is represented by the norm of vector and the extra SSR or partial determinant coefficient is represented by the angle between two vectors. Some lines are dotted when the partial F test results are statistically significant, so that statistical analysis could be explored. This geometrical description can be obtained the final regression models based on the forward selection and backward elimination methods. And the goodness-of-fit for the model could be explored.

• The Korean Journal of Applied Statistics
• /
• v.23 no.1
• /
• pp.73-79
• /
• 2010

Missing values for unit root processes are imputed by the most recent observations. Treating the imputed observations as if they are complete ones, semiparametric unit root tests are extended to missing value situations. Also, an invariance principle for the partial sum process of the imputed observations is established under some mild conditions, which shows that the extended tests have the same limiting null distributions as those based on complete observations. The proposed tests are illustrated by analyzing an unequally spaced real data set.