학급 규모 자료의 불연속 확률밀도함수의 추정

허집 한국데이터정보과학회 2023 한국데이터정보과학회지 Vol.34 No.1

When the probability density function has a discontinuity point, Huh (2002) proposed a kernel estimator of the location and the jump size of the discontinuity point, and showed their asymptotic properties. The hypothesis testing method for the existence of a discontinuity point was explained using the asymptotic distribution of the proposed jump size estimator. On the other hand, Cline and Hart (1999) proposed a kernel estimator of the discontinuous probability density function using the method of Schuster (1985) because the discontinuity point has the same problem as the boundary point in the kernel estimator. Huh (2002) separated samples based on discontinuity points and estimated the discontinuous probability density function with a boundary kernel function. In this study, we introduce an algorithm for estimating the number of discontinuity points in the probability density function using the hypothesis testing method for the existence of discontinuity point introduced by Huh (2002). By the algorithm, the number of discontinuity points are estimated in the probability density function of the 5th grade class size data in Angrist and Lavy (1999). The probability density function of the class size data is estimated and analyzed using the estimated the number and the locations of discontinuity points. 확률밀도함수가 불연속점을 가지는 경우에 Huh (2002)는 불연속점의 위치와 점프크기의 커널추정량을 제안하고 그들의 점근 성질을 보였다. 더불어, 제안한 점프크기 추정량의 점근 분포로 불연속점의 존재 여부에 대한 가설검접 방법을 설명하였다. 한편, Cline과 Hart (1991)는 불연속점은 커널추정량에서 경계점이 가지는 문제점과 동일한 문제점을 가지고 있기에 Schuster (1985)의 방법을 이용하여 불연속 확률밀도함수의 커널추정량을 제안하였다. Huh (2002)는 불연속점을 기준으로 표본을 분리하여 경계점에서 사용하는 커널함수로 불연속 확률밀도함수를 추정하였다. 본 연구에서는 Huh (2002)의 불연속점 존재 유무에 대한 가설검정 방법을 이용하여 확률밀도함수의 불연속점의 수를 추정하는 알고리듬을 소개하고, 이를 이용하여 Angrist와 Lavy (1999)에서 소개된 이스라엘 공립학교 5학년 학급 규모 자료의 확률밀도함수의 불연속점 수를 추정한다. 추정된 불연속점 수와 불연속점의 위치를 이용하여 학급 규모 자료의 확률밀도함수를 추정하고 분석하고자 한다.

계절별 저수지 유입량의 확률예측

강재원 ( Jae Won Kang ) 한국환경과학회 2013 한국환경과학회지 Vol.22 No.8

Reliable long-term streamflow forecasting is invaluable for water resource planning and management which allocates water supply according to the demand of water users. It is necessary to get probabilistic forecasts to establish risk-based reservoir operation policies. Probabilistic forecasts may be useful for the users who assess and manage risks according to decision-making responding forecasting results. Probabilistic forecasting of seasonal inflow to Andong dam is performed and assessed using selected predictors from sea surface temperature and 500 hPa geopotential height data. Categorical probability forecast by Piechota`s method and logistic regression analysis, and probability forecast by conditional probability density function are used to forecast seasonal inflow. Kernel density function is used in categorical probability forecast by Piechota`s method and probability forecast by conditional probability density function. The results of categorical probability forecasts are assessed by Brier skill score. The assessment reveals that the categorical probability forecasts are better than the reference forecasts. The results of forecasts using conditional probability density function are assessed by qualitative approach and transformed categorical probability forecasts. The assessment of the forecasts which are transformed to categorical probability forecasts shows that the results of the forecasts by conditional probability density function are much better than those of the forecasts by Piechota`s method and logistic regression analysis except for winter season data.

풍력발전기의 설비이용률 계산을 위한 확률밀도함수의 비교

강택근,허종철,좌종근 제주대학교 공과대학 첨단기술연구소 2003 尖端技術硏究所論文集 Vol.14 No.1

The Weibull probability density function and the Rayleigh function are compared by analyzing the capacity factors which are computed using the probability density functions with different mean wind speeds. For this analysis, the wind speed means of arithmetic, root mean square, cubic mean cuberoot, and standard deviations are computed from the measured wind speed data of a specific site, and the coefficients of probability density functions are calculated. The capacity factors for Vestas 850[kW] wind turbine are calculated and analyzed. The results show that the wind speed frequency curve by Rayleigh function is more close to the actual curve than by Weibull function. The more the wind speed frequency curve is close to the actual one, the more the capacity factors become large values.

A study on the fatigue damage model for Gaussian wideband process of two peaks by an artificial neural network

Kim, Y.,Kim, H.,Ahn, I.G. Pergamon Press 2016 Ocean engineering Vol.111 No.-

Calculations of the fatigue damage on marine structures with a wideband nature are difficult to be done in spectral approach point of view because the link between the spectrum of stress and the probability distribution is difficult to define. This paper addresses the methodology through which the functional relationship between the probability density function and the response spectrum of a bimodal wide-band process by using the artificial neural network technique. An artificial neural network scheme was used to identify the multivariate functional relationship between the two continuously varying functions. For this, the spectra were idealized as the superposition of two triangles with an arbitrary location, height and width and the probability density functions were represented by the linear combination of equally spaced Gaussian basis functions. To train the network under supervision, a variety of different wide-band spectra were assumed and the converged probability density function of the stress range was derived using the rainflow counting method and all these data sets were fed into the three layer perceptron model. It turned out that the network trained using the given data set could reproduce the probability density function of an arbitrary wide-band spectrum of two triangles with great success.

최대 엔트로피 방법을 이용한 비선형 불규칙 파고의 확률분포함수

안경모 한국해안해양공학회 1998 한국해안해양공학회 논문집 Vol.10 No.4

최대 엔트로피 방법을 이용하여 강한 비정규분포과정의 특성을 갖는 비선형 불규칙 파고의 확률밀도 함수를 유도하였다. 파랑의 파고가 쇄파고(또는 수심)에 의해 제한되고 파고의 1, 2차 모멘트만 주어졌을 경우, 유도된 확률밀도함수는 H_b (쇄파고), H_m(평균파고), H_rms(파고의 제곱평균평방근)의 매개변수로 폐합형(closed form)으로 표시된다. 파고의 3차 이상의 모멘트가 주어진 경우에는 최대 엔트로피를 갖는 확률밀도함수의 매개변수를 구하기 위해서 비선형 적분 방정식 계를 Newton-Raphson 방법을 이용하여 수치적으로 구하였다. 최대 엔트로피 방법을 이용하여 유도된 파고의 확률밀도함수를 비정규분포의 특성이 강한 실측자료와 비교하였다. 실측자료는 폭풍시 중간수심과 천해에서 측정된 쇄파고에 가까운 자료로서 강한 비선형 불규칙 파랑의 특성을 지니며, 이 경우에도 유도된 확률밀도함수가 측정된 파고의 막대그래프와 잘 일치하였다. 강한 비선형 불규칙파의 특성을 갖는 파랑의 파고일 경우에도 파고의 1, 2차 모멘트만으로도 파고의 분포를 잘 나타낼 수 있었다. 최대 엔트로피 방법을 이용하여 구해진 파고의 확률분포함수는 해안구조물의 설계파를 결정하는 극치파고분포와 파고의 통계적인 특성을 추정하는데 매우 유용하게 이용될 수 있다. This paper presents the development of the probability density function applicable for wave heights (peak-to-trough excursions) in finite water depth including shallow water depth. The probability distribution applicable to wave heights of a non-Gaussian random process is derived based on the concept of the maximum entropy method. When wave heights are limited by breaking wave heights (or water depth) and only first and second moments of wave heights are given, the probability density function developed is closed form and expressed in terms of wave parameters such as H_m(mean wave height), H_rms(root-mean-square wave height), H_b(breaking wave height). When higher than third moment of wave heights are given, it is necessary to solve the system of nonlinear integral equations numerically using Newton-Raphson method to obtain the parameters of probability density function which is maximizing the entropy function. The probability density function thusly derived agrees very well with the histogram of wave heights in finite water depth obtained during storm. The probability density function of wave heights developed using maximum entropy method appears to be useful in estimating extreme values and statistical properties of wave heights for the design of coastal structures.

Online Probability Density Estimation of Nonstationary Random Signal using Dynamic Bayesian Networks

Hyun Cheol Cho,M. Sami Fadali,Kwon Soon Lee 대한전기학회 2008 International Journal of Control, Automation, and Vol.6 No.1

We present two estimators for discrete non-Gaussian and nonstationary probability density estimation based on a dynamic Bayesian network (DBN). The first estimator is for off-line computation and consists of a DBN whose transition distribution is represented in terms of kernel functions. The estimator parameters are the weights and shifts of the kernel functions. The parameters are determined through a recursive learning algorithm using maximum likelihood (ML) estimation. The second estimator is a DBN whose parameters form the transition probabilities. We use an asymptotically convergent, recursive, on-line algorithm to update the parameters using observation data. The DBN calculates the state probabilities using the estimated parameters. We provide examples that demonstrate the usefulness and simplicity of the two proposed estimators.

Implementation of time-efficient adaptive sampling function design for improved undersampled MRI reconstruction

Choi, J.,Kim, H. Elsevier 2016 Journal of magnetic resonance Vol.273 No.-

To improve the efficacy of undersampled MRI, a method of designing adaptive sampling functions is proposed that is simple to implement on an MR scanner and yet effectively improves the performance of the sampling functions. An approximation of the energy distribution of an image (E-map) is estimated from highly undersampled k-space data acquired in a prescan and efficiently recycled in the main scan. An adaptive probability density function (PDF) is generated by combining the E-map with a modeled PDF. A set of candidate sampling functions are then prepared from the adaptive PDF, among which the one with maximum energy is selected as the final sampling function. To validate its computational efficiency, the proposed method was implemented on an MR scanner, and its robust performance in Fourier-transform (FT) MRI and compressed sensing (CS) MRI was tested by simulations and in a cherry tomato. The proposed method consistently outperforms the conventional modeled PDF approach for undersampling ratios of 0.2 or higher in both FT-MRI and CS-MRI. To fully benefit from undersampled MRI, it is preferable that the design of adaptive sampling functions be performed online immediately before the main scan. In this way, the proposed method may further improve the efficacy of the undersampled MRI.

Neutrosophic Conditional Probabilities: Theories and Applications

Ahmad M. H. Al-khazaleh,Shawkat Alkhazaleh 한국지능시스템학회 2022 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.22 No.1

Data could be uncertain, and the levels of precision of data are intuitively different. Neutrosophic set expressions are considered an alternative to represent imprecise data in such cases. In this paper, a general definition of neutrosophic conditional probability is introduced as a generalization of the classical conditional probability. Additionally, the properties of this neutrosophic conditional probability are presented. The concepts of joint distribution function, regular conditional probabilities, marginal density function, expected value, and joint density function in the classical type are generalized to a neutrosophic type with two discrete and continuous neutrosophic random variables. Various properties and examples are presented to demonstrate the significance of this study.

INCOMPLETE EXTENDED HURWITZ-LERCH ZETA FUNCTIONS AND ASSOCIATED PROPERTIES

Parmar, Rakesh K.,Saxena, Ram K. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.2

Motivated mainly by certain interesting recent extensions of the generalized hypergeometric function [Integral Transforms Spec. Funct. 23 (2012), 659-683] by means of the incomplete Pochhammer symbols $({\lambda};{\kappa})_{\nu}$ and $[{\lambda};{\kappa}]_{\nu}$, we first introduce incomplete Fox-Wright function. We then define the families of incomplete extended Hurwitz-Lerch Zeta function. We then systematically investigate several interesting properties of these incomplete extended Hurwitz-Lerch Zeta function which include various integral representations, summation formula, fractional derivative formula. We also consider an application to probability distributions and some special cases of our main results.

Prediction of Land Use/Land Cover Change in Forest Area Using a Probability Density Function

박진우,박정묵,이정수 강원대학교 산림과학연구소 2017 Journal of Forest Science Vol.33 No.4

This study aimed to predict changes in forest area using a probability density function, in order to promote effective forest management in the area north of the civilian control line (known as the Minbuk area) in Korea. Time series analysis (2010 and 2016) of forest area using land cover maps and accessibility expressed by distance covariates (distance from buildings, roads, and civilian control line) was applied to a probability density function. In order to estimate the probability density function, mean and variance were calculated using three methods: area weight (AW), area rate weight (ARW), and sample area change rate weight (SRW). Forest area increases in regions with lower accessibility (i.e., greater distance) from buildings and roads, but no relationship with accessibility from the civilian control line was found. Estimation of forest area change using different distance covariates shows that SRW using distance from buildings provides the most accurate estimation, with around 0.98-fold difference from actual forest area change, and performs well in a Chi-Square test. Furthermore, estimation of forest area until 2028 using SRW and distance from buildings most closely replicates patterns of actual forest area changes, suggesting that estimation of future change could be possible using this method. The method allows investigation of the current status of land cover in the Minbuk area, as well as predictions of future changes in forest area that could be utilized in forest management planning and policymaking in the northern area.