• 한국수학교육학회지시리즈B:순수및응용수학
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• 제5권2호
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.

• 한국경영과학회지
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• 제26권4호
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• pp.71-82
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• 2001

Using the computer simulation method, we invest19ate the probability distribution of maximum eigenvalue of pair-wise comparison matrix, which has been used as a parameter for measuring the consistency of responses in analytic hierarchy process (AHP). We show that the shape of the distribution of the maximum eigenvalue is different according to the dimension of the matrix. In addition, we cannot find any evidence that the distribution of the Consistency Index is a Normal distribution, which has been claimed in the Previous literature. Accordingly, we suggest using so called K-index calcu1ated based on the concept of cumulative distribution function lather than based on that of arithmetic mean because the probabilistic distribution cannot be assumed to be a Normal distribution. We interpret the simulation results by comparing them with the suggestion of Saaty[11]. Our results show that using Saaty＇s value could be too generous when the dimension of the matrix is 3 and strict over 4. Finally, we propose new criteria for measuring the response consistency in AHP.

• 상하수도학회지
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• 제34권4호
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• pp.251-258
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• 2020

Sewer deterioration models are needed to forecast the remaining life expectancy of sewer networks by assessing their conditions. In this study, the serious defect (or condition state 3) occurrence probability, at which sewer rehabilitation program should be implemented, was evaluated using four probability distribution functions such as normal, lognormal, exponential, and Weibull distribution. A sample of 252 km of CCTV-inspected sewer pipe data in city Z was collected in the first place. Then the effective data (284 sewer sections of 8.15 km) with reliable information were extracted and classified into 3 groups considering the sub-catchment area, sewer material, and sewer pipe size. Anderson-Darling test was conducted to select the most fitted probability distribution of sewer defect occurrence as Weibull distribution. The shape parameters (β) and scale parameters (η) of Weibull distribution were estimated from the data set of 3 classified groups, including standard errors, 95% confidence intervals, and log-likelihood values. The plot of probability density function and cumulative distribution function were obtained using the estimated parameter values, which could be used to indicate the quantitative level of risk on occurrence of CS3. It was estimated that sewer data group 1, group 2, and group 3 has CS3 occurrence probability exceeding 50% at 13th-year, 11th-year, and 16th-year after the installation, respectively. For every data groups, the time exceeding the CS3 occurrence probability of 90% was also predicted to be 27th- to 30th-year after the installation.

• 한국분무공학회지
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• 제20권3호
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• pp.175-180
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• 2015

A series of sprinkler discharging tests was conducted to measure the droplet size and its distribution of residential fire sprinkler heads. Droplet sizes in sprinkler spray were measured using a laser diffraction method for the flush, circular and pendent type sprinkler head. In this study, the $D_{v,50}$ of the flush type sprinkler heads were ranged between $530{\sim}1040{\mu}m$ and those of circular and pendent type were $988{\mu}m$ and $916{\mu}m$, respectively. The measured cumulative volume distributions were followed by a combination of the log-normal and Rosin-Rammler distribution which is widely used in the computational fire analysis and the parameters of distribution function were obtained from the best fit line through the measured data.

• KSII Transactions on Internet and Information Systems (TIIS)
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• 제10권6호
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• pp.2567-2582
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• 2016

This paper investigates the impact of outdated channel state information (CSI) on the performance of the incremental amplify-and-forward (AF) opportunistic relaying (OR) over dual-hop Rayleigh fading channels. According to the definition of distribution function, we obtain the cumulative distribution function (CDF) of the actual combined signal-to-noise ratio (SNR) received at the destination. Based on this CDF, the closed-form expressions of the average spectral efficiency and outage probability are derived for the incremental AF OR under outdated CSI. Numerical results show that in the low region of the average SNR of the direct link, outdated CSI deteriorates the system performance, whereas in the high region, outdated CSI has almost no impact on the system performance.

• International Journal of Automotive Technology
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• 제8권5호
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• pp.563-573
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• 2007

Optimal design of an automotive catalytic converter for minimization of cold-start emissions is numerically performed using a micro genetic algorithm for two optimization problems: optimal geometry design of the monolith for various operating conditions and optimal axial catalyst distribution. The optimal design process considered in this study consists of three modules: analysis, optimization, and control. The analysis module is used to evaluate the objective functions with a one-dimensional single channel model and the Romberg integration method. It obtains new design variables from the control module, produces the CO cumulative emissions and the integral value of a catalyst distribution function over the monolith volume, and provides objective function values to the control module. The optimal design variables for minimizing the objective functions are determined by the optimization module using a micro genetic algorithm. The control module manages the optimal design process that mainly takes place in both the analysis and optimization modules.

• 정보처리학회논문지B
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• 제16B권4호
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• pp.263-270
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• 2009

히스토그램 평활화는 주어진 입력 영상의 누적분포함수 CDF (Cumulative Distribution Function)를 이용하여 영상의 동적영역 (Dynamic Range)을 확장하고 히스토그램의 분포를 균등하게 함으로써 명암비를 개선한다. 그러나 히스토그램 평활화는 영상의 밝기를 과도하게 변하게 하는 단점이 있다. 본 논문에서는 과도한 명암비 향상을 억제하기위해 서브-히스토그램의 면적비 기반의 히스토그램 재분배를 이용한 적응형명암비 향상 알고리즘. 제안한 알고리즘은 영상의 동적영역을 입력영상의 휘도 평균값을 기반으로 분할하고, 분할된 영역의 면적비에 따라 밝기 분포를 재분배함으로써 과도한 밝기 변화를 효과적으로 억제 할 수 있다. 실험결과를 통하여 시각적으로 색의 왜곡이 없는 자연스러운 영상을 확인하였고, 평균값의 비교를 통해 과도한 밝기 변화를 억제한 것을 확인 할 수 있었다. 또한 히스토그램의 분포에 상관없이 대부분의 영상에서 우수한 결과를 나타내는 것을 실험결과에서 알 수 있었다.

• 정보과학회 컴퓨팅의 실제 논문지
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• 제20권12호
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• pp.646-651
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• 2014

히스토그램 평활화는 영상의 밝기 값 분포가 한 곳에 밀집되어 있는 경우, 출력영상의 밝기 값 범위가 지나치게 확장되어 시각적으로 부자연스러운 결과를 초래하는 단점을 가지고 있다. 그런데 감마변환은 이런 부자연스러운 현상을 비선형적 변환을 통해 보정해주는 성질을 가지고 있다. 따라서 본 논문에서는 감마변환의 이런 성질을 이용하여 영상의 화질을 개선하는 새로운 히스토그램 평활화 방법을 제안한다. 제안 방법은 먼저, 입력영상의 평균 밝기 값을 이용하여 적절한 감마변환 식을 도출하고, 입력영상의 CDF(Cumulative Distribution Function)를 도출된 감마변환 식과 선형 결합하여 새로운 CDF를 생성한 후, 새롭게 변형된 CDF를 사용하여 히스토그램 평활화를 수행한다. 실험결과 제안방법이 기존방법들에 비해 entropy, UIQ, SSIM 등과 같은 정량적 평가에서 좋은 성능을 보였고, 시각적 관점에서도 자연스럽게 화질을 개선하였다.

• 한국화재소방학회논문지
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• 제20권1호
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• pp.6-14
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• 2006

가스로 인한 화재 및 폭발사고의 예측 가능한 프로그램을 구체화하고, 적절한 사회적 위험기준을 제시하기 위하여 최근 11년간의 가스사고 데이터베이스를 분석하였다. 먼저 동일유형의 가스사고 발생가능 성을 판단할 수 있는 Poisson 분석 방법을 적용하기 위해 3개의 사고유형, 즉 누출, 폭발, 화재로 구분하여 총 16개 항목으로 나누어서 적용하였다. 그 결과, 시공 작업 부주의-폭발-배관의 항목의 사고발생반도가 가장 작았으며, 배관연결부이완부식-누출-배관의 경우는 가장 높은 빈도를 나타내었다. 따라서 이에 대한 적절한 가스사고 대응책이 마련되어야 할 것이다. 또한 치명적인 가스사고의 추세와 합리적인 위험정책에 대한 지침을 결정하기위해 D. O. Hagon 방정식과 회기직선식을 이용하여 F.N 곡선의 누적사망자의 최소 및 최대점에 대응시켜 허용가능영역을 설정하였다. 향후 가스사고에 대한 신뢰성 있는 분석을 위해서는 가스로 인한 화재 폭발사고에 대한 데이터베이스를 지속적으로 확충보완을 시켜야 되며, 이를 위한 표준 코드화 작업이 요구된다.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.