• Journal of the Korean Statistical Society
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• 제26권3호
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• pp.289-297
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• 1997

It is well known that the spacings, the differences of two successive order statistics, in a random sample of size n from a distribution function F are independent and exponentially distributed if F is itself the exponential distribution. In this paper we obtain an asymptotically similar result on a fixed number of upper spacings as n .to. .infty. for a general F under the assumption that F is in the domain of attraction of some extreme value distribution. For a heavy or short tailed F, appropriate log transformations of the sample should be proceded to get the result. As a by-product, we also get that each upper spacing diverges in probability to .infty. and converges in probability to 0 as n .to. .infty. for a heavy and short tailed F, respectively, which is fully expected.

• Journal of the Korean Statistical Society
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• 제22권1호
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• pp.13-25
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• 1993

The purpose of this paper is to investigate the properties of order statistics under various stochastic relations. We study the stochastic comparison of order statistics in a single sample. And we consider two sample case too. For example, F(t) > G9t) for t > 0 when X and Y are random variables symmetric about 0, with c.d.f.s F and G. Two examples are provided.

• 대한수학회보
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• 제31권1호
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• pp.45-54
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• 1994

Throughout this paper, the definitions and properities related to probabilistic normed spaces are followed as in [2]. Let R be the set of all real numbers. A mapping F:R .rarw. [0, 1] is called a distribution function on R if it is nondecreasing and left continuous with inf F = 0 and sup F = 1. We denote by L the set of all distribution functions on R.

• 품질경영학회지
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• 제29권2호
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• pp.37-45
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• 2001

A survival variable is a non-negative random variable X with distribution function F(t) satisfying F(0) : 0 and a survival function F(t): 1-F(t). This variable is said to be New Better than Used of specified age t$_{0}$ if F(x+ t$_{0}$)$\leq$F(x).F(t$_{0}$) for all x$\geq$0 and a fixed t$_{0}$. We propose the test for H$_{0}$ : F(x+t$_{0}$)=F(x).F(t$_{0}$) for all x$\geq$0 against H$_1$: F(x+t$_{0}$) $\leq$ F(x).F(t$_{0}$) for all x$\geq$0 when the specified age to is unknown but can be estimated from the data when t$_{0}$=ζ$_{p}$, the pth percentile of F. This test statistic, which is based on the normalized spacings between the ordered observations, is readily applied in the case of small sample. Also, our test is more simple than Ahmad's test (1998). Finally, the performance of our test is presented.our test is presented.

• Asian-Australasian Journal of Animal Sciences
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• 제13권6호
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• pp.733-738
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• 2000

The objective of this study was to describe the nature of the inheritance of jumping as a behavioral trait and to analyze quantitatively the jumping height as a measure of vigor in two subspecies of mice. Two subspecies of mice, Yonakuni wild mouse (Y) and $CF_{{\sharp}1}$ laboratory mouse (C), were used as the parental types. Reciprocal mating between these two subspecies was made to produce subsequently the first and second generations. The first generation was $F_1$ (YC) resulting from $Y\;male{\times}C\;female$, and $F_1{^\prime}$ (CY) from $C\;male{\times}Y\;female$. The second generation $F_2$ (YCYC) was from mating $F_1{\times}F_1$ and $F_2{^\prime}$ (CYCY) from $F_1{^\prime}{\times}F_1{^\prime}$. Individuals were treated with a set of direct current shock apparatus at six weeks of age to evoke jumping. The results showed that the ratio between jumping and non jumping mice (J: NJ) for C was 0%:100% (0:1), which means that all C did not jump throughout the experiment, whereas Y was 68%:32% (2:1); and the $F_1$ and $F_2$ showed 65%:35% (2:1) and 51%:49% (1:1), respectively. All $F_1{^\prime}$ and $F_2{^\prime}$ individuals jumped as indicated by the ratio 100%:0% (1:0) for both these two genetic groups. Of the jumped mice, average height of the first three jumping observed for pooled sexes in Y, $F_1$, $F_2$, $F_1{^\prime}$ and $F_2{^\prime}$ were 19.3 cm, 19.3 cm, 18.0 cm, 19.9 cm and 16.4 cm, respectively. The distribution of jumping height showed a tendency to be a normal distribution. The jumping activity and jumping height may be affected by some major genes and polygenes, respectively.

• 농업과학연구
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• 제22권2호
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• pp.163-169
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• 1995

본 연구는 홀스타인종 유우의 혈청단백질 및 효소에 대한 유전적 구조를 분석하기 위하여, 혈청단백질인 post-transferrin-2(pTf-2), transferrin(Tf), post-albumin(pAlb) 및 albumin(Alb)과 혈청효소인 ceruloplasmin(Cp)와 amylase-I(Am-I)을 polyacrylamide gel electrophoresis(PAGE)와 starch g디 electrophoresis(STAGE) 방법으로 유전적 변이체를 분석하였다. 혈청단백질인 pTf-2 좌위는 pTf-2 F와 S 유전자에 의해 지배되는 pTf-2 FF, FS 및 SS 유전자형이 확인되었으며, 이들의 분포는 각각 76.34%, 14.50% 및 9.10%이었고, 유전자빈도는 pTf-2 F와 S가 각각 0.836 및 0.164이었다. 한편 Tf 좌위는 Tf A, D1, D2 및 E 유전자가 검출되었으며, 유전자형은 Tf AA, AD1, AD2, AE, D1D1, D1D2, D2D2 및 D2E형이 확인되었고, 이들의 분포는 각각 0.11, 32.06, 19.08, 1.53, 10.69, 18.32, 9.92 및 2.29%이었으며, 유전자빈도는 Tf A, D1, D2 및 E에서 각각 0.324, 0.359, 0.298 및 0.019이었다. 또한 pAlb 좌위는 pAlb F와 S 유전자가 검출되었고, 유전자형은 pAlb FF, FS 및 SS형이 확인되었으며, 이들의 분포는 각각 32.06, 29.77 및 38.17%이었고, 유전자빈도는 pAlb F와 S가 각각 0.469 및 0.531이었다. Alb 유전자 빈도에 있어서는 Alb A와 B가 각각 0.996 및 0.004이었다. 그리고 혈청효소인 Cp 좌위는 Cp F와 S 유전자가 검출되었으며, 유전자형은 Cp FF, FS 및 SS 형이 확인되었고, 이들의 분포는 각각 46.57, 27.48 및 25.95%이었으며, 유전자빈도는 Cp F와 S가 각각 0.603 및 0.394이었다. Am-I 좌위는 Am-I B와 C 유전자가 검출되었으며, 유전자형은 Am-I BB, BC 및 CC 형이 확인되었고, 이들의 빈도비율은 각각 39.69, 21.73 및 38.93% 이었으며, 유전자 빈도는 Am-I B와 C가 각각 0.503 및 0.497이었다.

• 한국환경과학회지
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• 제30권12호
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• pp.983-991
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• 2021

The role of the distribution basin role is to apportion incoming raw water to the primary sedimentation basin as part of the water treatment process. The purpose of this study was to calculate the amount of water in the distribution basin using computational fluid dynamics (CFD) analysis and to find a way to improve any non-uniformity. We used the Taguchi method and the minitab tool as optimization methods. The results of the CFD calculation showed that the distribution flow had a deviation of 5% at the minimum inflow, 10% at the average inflow, and 22% at the maximum inflow. At maximum flow, the appropriate heights of the 7 weirs(C, D, A, B, E, F, G) were 40 mm, 20 mm, 20 mm, 0, 0, 0, and 20 mm, respectively, according to the Taguchi optimization tool. Here, the maximum deviation of the distribution amount was 9% and the standard deviation was 23.7. The appropriate heights of the 7 weirs, according to the Minitab tool, were 40 mm, 20 mm, 20 mm, 0, 0, 0, and 20 mm, respectively, for weirs C, D, A, B, E, F, and G. Therefore, the maximum deviation of the distribution amount was 8% and the standard deviation was 17.1, which was slightly improved compared to the Taguchi method.

• Bulletin of the Korean Chemical Society
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• 제23권2호
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• pp.229-240
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• 2002

Quantum mechanical calculation is performed for the $O(^1D)$ + HCl ${\rightarrow}$OH + Cl reaction using Reactive Infinite Order Sudden Approximation. Shifting approximation is also employed for the l ${\neq}$ 0 partial wave contributions. Various dynamical quantities are calculated and compared with available experimental results and quasiclassical trajectory results. Vibrational distributions agree well with experimental results i.e. product states mostly populated at $v_f$ = 3, 4. Our results also show small peak at $v_f$ = 0, which indicates bimodal vibrational distribution. The results show two significant broad peaks in ${\gamma}_i$ dependence of the cross section, one is at ${\gamma}_i$ = $15^{\circ}-35^{\circ}$ and the another is at ${\gamma}_i$= $55^{\circ}-75^{\circ}$ which can be explained as steric effects. At smaller gi, the distribution is peaked only at higher state ($v_f$ = 3, 4) while at the larger gi, both lower state ($v_f$ = 0) and higher state ($v_f$ = 3, 4) are significantly populated. Such two competing contributions (smaller and larger ${\gamma}_i$) result in the bimodal distribution. From these points we suggest two mechanisms underlying in current reaction system: one is that reaction occurs in a direct way, while the another is that reaction occurs in a indirect way.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.441-446
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• 2003

Let { $X_{n}$ , n $\geq$ 1} be a sequence of independent and identically distributed random variables with a common continuous distribution function F(x) and probability density function f(x). Let $Y_{n}$ = max{ $X_1$, $X_2$, …, $X_{n}$ } for n $\geq$ 1. We say $X_{j}$ is an upper record value of { $X_{n}$ , n$\geq$1} 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$\geq$1, where u(n) = min{j｜j>u(n-1), $X_{j}$ > $X_{u}$ (n-1), n$\geq$2} and u(1) = 1. We call the random variable X $\in$ Beta (1, c) if the corresponding probability cumulative function F(x) of x is of the form F(x) = 1-(1-x)$^{c}$ , c>0, 0$\leq$x$\leq$1. In this paper, we will give a characterization of the beta distribution of the first kind by considering conditional expectations of record values.s.

• 대한치과교정학회지
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• 제45권4호
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• pp.198-208
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• 2015

Objective: To quantify, for each activation, the effect of preactivations of differing distribution and intensity on the neutral position of T-loops (7-mm height), specifically the horizontal force, moment to force (M/F) ratio, and load to deflection ratio. Methods: A total 100 loops measuring $0.017{\times}0.025$ inches in cross-section were divided into two groups (n = 50 each) according to composition, either stainless steel or beta-titanium. The two groups were further divided into five subgroups, 10 loops each, corresponding to the five preactivations tested: preactivations with occlusal distribution ($0^{\circ}$, $20^{\circ}$, and $40^{\circ}$), gingival distribution ($20^{\circ}$), and occlusal-gingival distribution ($40^{\circ}$). The loops were subjected to a total activation of 6-mm with 0.5-mm iterations. Statistical analysis was performed using comprised ANOVA and Bonferoni multiple comparison tests, with a significance level of 5%. Results: The location and intensity of preactivation influenced the force intensity. For the M/F ratio, the highest value achieved without preactivation was lower than the height of the loop. Without preactivation, the M/F ratio increased with activation, while the opposite effect was observed with preactivation. The increase in the M/F ratio was greater when the preactivation distribution was partially or fully gingival. Conclusions: Depending on the preactivation distribution, displacement of uprights is higher or lower than the activation, which is a factor to consider in clinical practice.