• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.299-303
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• 1998

In this paper weak laws of large numbers are obtained for random variables in $L^{1}(R)$ which satisfy a compact uniform integrability condition.

• Journal of the Korean Statistical Society
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• 제23권1호
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• pp.39-51
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• 1994

Some exponential moment inequalities for sub-gaussian random variables are studied in this paper. These inequalities are used to obtain laws of large numbers for random variable and random elements in $L^1(R)$.

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.347-349
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• 1995

In this paper a central limit theorem on $L^P(R)$ for $1{\leq}p<{\infty}$ is obtained with an example when ${X_n}$ is a sequence of independent, identically distributed random variables on $L^P(R)$.

• 대한수학회보
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• 제47권3호
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• pp.467-482
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• 2010

For a double array of random elements {$V_{mn};m{\geq}1,\;n{\geq}1$} in a real separable Banach space, some mean convergence theorems and weak laws of large numbers are established. For the mean convergence results, conditions are provided under which $k_{mn}^{-\frac{1}{r}}\sum{{u_m}\atop{i=1}}\sum{{u_n}\atop{i=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in $L_r$ (0 < r < 2). The weak law results provide conditions for $k_{mn}^{-\frac{1}{r}}\sum{{T_m}\atop{i=1}}\sum{{\tau}_n\atop{j=1}}(V_{ij}-E(V_{ij}|F_{ij})){\rightarrow}0$ in probability where {$T_m;m\;{\geq}1$} and {${\tau}_n;n\;{\geq}1$} are sequences of positive integer-valued random variables, {$k_{mn};m{{\geq}}1,\;n{\geq}1$} is an array of positive integers. The sharpness of the results is illustrated by examples.

• 대한수학회지
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• 제36권6호
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• pp.1133-1143
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• 1999

Chaterji strengthened version of a theorem for martin-gales which is a generalization of a theorem of Marcinkiewicz proving that if $X_n$ is a sequence of independent, identically distributed random variables with $E{\mid}X_n{\mid}^p\;<\;{\infty}$, 0 < P < 2 and $EX_1\;=\;1{\leq}\;p\;<\;2$ then $n^{-1/p}{\sum^n}_{i=1}X_i\;\rightarrow\;0$ a,s, and in $L^p$. In this paper, we probe a version of law of large numbers for double arrays. If ${X_{ij}}$ is a double sequence of random variables with $E{\mid}X_{11}\mid^log^+\mid X_{11}\mid^p\;<\infty$, 0 < P <2, then $lim_{m{\vee}n{\rightarrow}\infty}\frac{{\sum^m}_{i=1}{\sum^n}_{j=1}(X_{ij-a_{ij}}}{(mn)^\frac{1}{p}}\;=0$ a.s. and in $L^p$, where $a_{ij}$ = 0 if 0 < p < 1, and $a_{ij}\;=\;E[X_{ij}\midF_[ij}]$ if $1{\leq}p{\leq}2$, which is a generalization of Etemadi's marcinkiewicz-type SLLN for double arrays. this also generalize earlier results of Smythe, and Gut for double arrays of i.i.d. r.v's.

• 한국농공학회지
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• 제22권3호
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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.

• 한국운동역학회지
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• 제30권4호
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• pp.301-309
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• 2020

Objective: This study aimed to investigate the effect of white noise on dynamic balance in patients with stroke during walking. Method: Nineteen patients with chronic stroke (age: 61.2±9.8 years, height: 164.4±7.4 cm, weight: 61.1±9.4 kg, paretic side (R/L): 11/8, duration: 11.6±4.9 years) were included as study participants. Auditory stimulus used white noise, and all participants listened for 40 minutes mixing six types of natural sounds with random sounds. The dynamic balancing ability was evaluated while all participants walked before and after listening to white noise. The variables were the center of pressure (CoP), the center of mass (CoM), CoP-CoM inclined angle. Results: There is a significant increase in the antero-posterior (A-P) CoP range, A-P inclination angle, and gait speed on the paretic and non-paretic sides following white noise intervention (p<.05). Conclusion: Our findings confirmed the positive effect of using white noise as auditory stimulus through a more objective and quantitative assessment using CoP-CoM inclination angle as an evaluation indicator for assessing dynamic balance in patients with chronic stroke. The A-P and M-L inclination angle can be employed as a useful indicator for evaluating other exercise programs and intervention methods for functional enhancement of patients with chronic stroke in terms of their effects on dynamic balance and effectiveness.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제11권1호
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• pp.97-102
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• 2004

In this paper we establish some recurrence relations satisfied by quotient moments of upper record values from the Pareto distribution. Let ｛$X_n,n\qeq1$｝be a sequence of independent and identically distributed random variables with a common continuous distribution function(cdf) F($chi$) and probability density function(pdf) f($chi$). Let $Y_n\;=\;mas{X_1,X_2,...,X_n}$ for $ngeq1$. We say $X_{j}$ is an upper record value of {$X_{n},n\geq1$}, if $Y_{j}$＞$Y_{j-1}$,j＞1. The indices at which the upper record values occur are given by the record times ${u( n)}n,\geq1$, where u(n) = min{j｜j ＞u(n-l), $X_{j}$＞$X_{u(n-1)}$,n\qeq2$ and u(l) = 1. Suppose $X{\epsilon}PAR(\frac{1}{\beta},\frac{1}{\beta}$ then E$(\frac{{X^\tau}}_{u(m)}}{{X^{s+1}}_{u(n)})\;=\;\frac{1}{s}E$ E$(\frac{{X^\tau}}_{u(m)}{{X^s}_{u(n-1)}})$ - $\frac{(1+\betas)}{s}E(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}}$ and E$(\frac{{X^{\tau+1}}_{u(m)}}{{X^s}_{u(n)}})$ = $\frac{1}{(r+1)\beta}$ [E$(\frac{{X^{\tau+1}}}_u(m)}{{X^s}_{u(n-1)}})$ - E$(\frac{{X^{\tau+1}}_u(m)}}{{X^s}_{u(n-1)}})$ - (r+1)E$(\frac{{X^\tau}_{u(m)}}{{X^s}_{u(n)}})$]

• 한국동물학회지
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• 제31권4호
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• pp.327-333
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• 1988

계절에 따른 초파리 집단내 역위다형 현상의 변동상을 알기 위하여 전주근교의 과수원에서 1983년 1월부터 11월까지 격월로 여섯번 채집한 집단 표본을 분석하였다. 총 1071마리에서 얻은 15개형의 역위는 모두 편동원체역위(paracentric inversion)였으며, 이 중 7개형은 세계형91위(cosmopolitan inversion)였고, 나머지 8개형은 지역형역위(endemic inversion)였다. 개체당 역위의 평균 보유수는 0.639이고 역위를 보유한 개체의 빈도는 0.465였다. 7개의 세계형역위에 대한 표본집단을 분석한 결과 격월 집단간에서 유의한 차이를 보이는 반면 1월과 1 1월 표본간에서는 그 성황이 오히려 비숫해짐으로서 집단내 총역위빈도는 주기적으로 변동하고 있음이 암시된다. 역위와 환경변수와의 다중상관분석에서는 기온, 습도, 강수량이 역위빈도에 유의한 영향을 미치는 것으로 나타났고 역위 중 In(2L)t가 상기한 환경변수 모두에 대하여 유의한 상관관계를 보인 반면, In(3R)C와 In(3R)P는 어느 것과도 상관성을 보이지 않았다. 염색체내 그리고 염색체간의 연관 또는 조합의 검정결과 연관불평형혈상을 1월, 5월, 그리고 7월 표본의 제3염색체에서, 그리고 비균일조합은 1월과 7월 표본에서 역시 제3염색체에서만 산출 되었다. Seasonal changes of inversion frequencies in Chonju 0. melanogaster populations were studied. A total of 1071 males were collected six times with ho months intewal from January through November in 1983. to analyse diploid sets of chromosomes carried by males, each male was mated to several virgin females homoBvgous for cytologically standard sequence in all chromo-somes. From each mating, more than seven FL larvae were selected in random and tested to find chromosomal aberrations. In the present study, 15 different inversions were found and identified to be paracentric only In both second and third chromosomes; seven were cosmopolitan and the rest eight endemic types. The average frequency of inversions was 0.465 and the mean number of inversions carried by a single male was 0.639. The linkage disequilibria were detected between the leK and right arms of third chromosomes from the samples of January, May and Julv, Whereas nonrandom associations appeared also in the third chromosomes only in January and Julv samples. In multiple regression analysis among frequencies of inversions and environ-mental variables it appeared that mean temperature, relative humidity and total precipitation for a month skipped over 30 days before collected affect to change to frequencies of particular inver-sions. With respect to the behavior of inversions in the present samples, it is suggested, with the Friedman's analysis of variance by ranks of inversion frequency orders, that the frequencies of inversions change cyclically year to year.

• 대한원격탐사학회지
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• 제39권5_3호
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• pp.933-948
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• 2023

대기 중 에어로졸은 인체에 악영향을 끼칠 뿐 아니라 기후 시스템에도 직간접적인 영향을 미치므로 에어로졸의 특성과 시공간적인 분포에 대한 이해는 매우 중요하다. 이를 위해 위성기반 관측을 통해 에어로졸 광학 두께(Aerosol Optical Depth, AOD)를 산출하여 에어로졸을 모니터링하는 다양한 연구가 수행되어 왔다. 하지만 이는 주로 조견표를 활용한 역 산출 알고리즘에 기반하여 이루어지기 때문에 많은 계산량을 요구하며 불확실성이 존재한다. 따라서, 본 연구에서는 Geostationary Ocean Color Imager-II (GOCI-II)의 대기상한반사도와 30일 동안의 대기상한반사도 중 최솟값과 관측 시점 값의 차이 값, 수치 모델 기반 기상학적 변수 등을 활용하여 기계학습 기반 고해상도 AOD 직접 산출 알고리즘을 개발하였다. Light Gradient Boosting Machine (LGBM) 기법이 사용되었으며, 추정된 결과는 지상 관측 자료인 Aerosol Robotic Network (AERONET) AOD를 활용하여 랜덤, 시간 및 공간별 N-fold 교차검증을 통해 검증되었다. 세 가지 교차검증 결과 R²=0.70-0.80, RMSE=0.08-0.09, 기대오차(Expected Error, EE) 안에 있는 비율은 75.2-85.1% 수준으로 안정적인 성능을 보였다. Shapley Additive exPlanations (SHAP) 분석에서는 반사도 관련 변수들이 기여도의 상위권 대부분을 차지하고 있는 것을 통해 반사도 자료가 AOD 추정에 많은 기여를 하는 것을 확인하였다. 서울과 울산 지역에 대한 시간 별 AOD의 공간 분포를 분석한 결과, 개발된 LGBM 모델은 시간의 흐름에 따라 AERONET AOD 값과 유사한 수준으로 AOD를 추정하고 있었다. 이를 통해 높은 시공간 해상도(i.e., 시간별, 250 m)에서의 AOD 산출이 가능함을 확인하였다. 또한, 산출 커버리지 비교에서 LGBM 모델의 평균 산출 빈도가 GOCI-II L2 AOD 산출물 대비 8.8%가량 증가한 것을 통해 기존 물리모델기반 AOD 산출 과정에서 발생하던 밝은 지표면에 대한 과도한 마스킹의 문제점을 개선시킨 것을 확인하였다.