• Magazine of the Korean Society of Agricultural Engineers
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• v.22 no.3
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• pp.75-87
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• 1980

Most hydro]ogic phenomena are the complex and organic products of multiple causations like climatic and hydro-geological factors. A certain significant correlation on the run-off in river basin would be expected and foreseen in advance, and the effect of each these causual and associated factors (independant variables; present-month rainfall, previous-month run-off, evapotranspiration and relative humidity etc.) upon present-month run-off(dependent variable) may be determined by multiple regression analysis. Functions between independant and dependant variables should be treated repeatedly until satisfactory and optimal combination of independant variables can be obtained. Reliability of the estimated function should be tested according to the result of statistical criterion such as analysis of variance, coefficient of determination and significance-test of regression coefficients before first estimated multiple regression model in historical sequence is determined. But some error between observed and estimated run-off is still there. The error arises because the model used is an inadequate description of the system and because the data constituting the record represent only a sample from a population of monthly discharge observation, so that estimates of model parameter will be subject to sampling errors. Since this error which is a deviation from multiple regression plane cannot be explained by first estimated multiple regression equation, it can be considered as a random error governed by law of chance in nature. This unexplained variance by multiple regression equation can be solved by stochastic approach, that is, random error can be stochastically simulated by multiplying random normal variate to standard error of estimate. Finally hybrid model on estimation of monthly run-off in nonhistorical sequence can be determined by combining the determistic component of multiple regression equation and the stochastic component of random errors. Monthly run-off in Naju station in Yong-San river basin is estimated by multiple regression model and hybrid model. And some comparisons between observed and estimated run-off and between multiple regression model and already-existing estimation methods such as Gajiyama formula, tank model and Thomas-Fiering model are done. The results are as follows. (1) The optimal function to estimate monthly run-off in historical sequence is multiple linear regression equation in overall-month unit, that is; Qn=0.788Pn+0.130Qn-1-0.273En-0.1 About 85% of total variance of monthly runoff can be explained by multiple linear regression equation and its coefficient of determination (R2) is 0.843. This means we can estimate monthly runoff in historical sequence highly significantly with short data of observation by above mentioned equation. (2) The optimal function to estimate monthly runoff in nonhistorical sequence is hybrid model combined with multiple linear regression equation in overall-month unit and stochastic component, that is; Qn=0. 788Pn+0. l30Qn-1-0. 273En-0. 10+Sy.t The rest 15% of unexplained variance of monthly runoff can be explained by addition of stochastic process and a bit more reliable results of statistical characteristics of monthly runoff in non-historical sequence are derived. This estimated monthly runoff in non-historical sequence shows up the extraordinary value (maximum, minimum value) which is not appeared in the observed runoff as a random component. (3) "Frequency best fit coefficient" (R2f) of multiple linear regression equation is 0.847 which is the same value as Gaijyama's one. This implies that multiple linear regression equation and Gajiyama formula are theoretically rather reasonable functions.

• Communications of the Korean Mathematical Society
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• v.26 no.1
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• pp.151-161
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• 2011

Let {$X_n$, $n{\geq}1$} be a sequence of asymptotically almost negatively associated random variables and $S_n=\sum^n_{i=1}X_i$. In the paper, we get the precise results of H$\acute{a}$jek-R$\acute{e}$nyi type inequalities for the partial sums of asymptotically almost negatively associated sequence, which generalize and improve the results of Theorem 2.4-Theorem 2.6 in Ko et al. ([4]). In addition, the large deviation of $S_n$ for sequence of asymptotically almost negatively associated random variables is studied. At last, the Marcinkiewicz type strong law of large numbers is given.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1139-1153
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• 2010

Let {$X_j,\;j\geq1$} be a strictly stationary $\phi$-mixing sequence of non-degenerate random variables with $EX_1$ = 0. In this paper, we establish a self-normalized weak invariance principle and a central limit theorem for the sequence {$X_j$} under the condition that L(x) := $EX_1^2I{|X_1|{\leq}x}$ is a slowly varying function at $\infty$, without any higher moment conditions.

• Journal of the Korean Statistical Society
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• v.24 no.1
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• pp.219-224
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• 1995

A central limit theorem with random indices is obtained for stattionary martingale difference sequences.

• Proceedings of the Korean Reliability Society Conference
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• 2002.06a
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• pp.303-303
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• 2002

We obtain the necessary and sufficient condition of tightness for a sequence of random variables in the space of fuzzy sets with compact support in R.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.117-123
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• 2005

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.1
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• pp.1-5
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• 2009

Let {$X_n,\;n{\geq}1}$ be a sequence of independent identically distributed(i.i.d.) sequence of positive random variables with common absolutely continuous distribution function(cdf) F(x) and probability density function(pdf) f(x) and $E(X^2)<{\infty}$. The random variables $\frac{X_i{\cdot}X_j}{(\Sigma^n_{k=1}X_k)^{2}}$ and $\Sigma^n_{k=1}X_k$ are independent for $1{\leq}i if and only if {$X_n,\;n{\geq}1}$ have gamma distribution.

• Journal of applied mathematics & informatics
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• v.22 no.1_2
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• pp.331-338
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• 2006

The Paley-type inequalities for the complete convergence and lower and upper bounds in the Baum-Katz law of large numbers for i.i.d. random variables sequence are obtained. The results obtained generalize the result of Pruss [8].

• Journal of the Korean Institute of Telematics and Electronics
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• v.18 no.4
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• pp.12-20
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• 1981

In this paper, Band-limlted Gaussian Random Noise and PRBS(pseudo random hinary sequence) are used as a test signals to estimate the dynamic characteristics of the ocuiomotor system. Eye movements of the human subject are measured by E.O.G(electro-oculography) and the control characteristics of the oculomotor system are studied by random signal an-alysis based on the statistical communication theory. The conclusions are summerized as follows. (1) From the frequency response, the gain curve rises slightly at the regions of 0.7~0.9 Hz and 1.8~2 Hz due to the saccades which are occurred during usual tracking. (2) The average rate of information transfer by the oculomotor control system is 1.24 bits/sec, being calculated from the power spectral density and the cross spectral density for the Gaussian random input.

• Honam Mathematical Journal
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• v.32 no.1
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• pp.91-99
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• 2010

In this paper we introduce the concept of asymptotically almost negatively associated random variables in a Hilbert space and obtain the strong law of large numbers for a strictly stationary asymptotically almost negatively associated sequence of H-valued random variables with zero means and finite second moments. As an application we prove a strong law of large numbers for a linear process generated by asymptotically almost negatively random variables in a Hilbert space with this result.