• ETRI Journal
• /
• 제32권6호
• /
• pp.965-968
• /
• 2010

In this letter, we derive the distribution functions of five ratios involving two correlated Gaussian random variables by using the rotation of Cartesian coordinates. The results can be used in evaluating the various probability performances of wireless communications systems.

• Structural Engineering and Mechanics
• /
• 제86권3호
• /
• pp.349-359
• /
• 2023

This paper presents a technique for determining the optimal number of elements in stochastic finite element analysis based on reliability analysis. Using the change-of-variable perturbation stochastic finite element approach, the probability density function of the dynamic responses of stochastic structures is explicitly determined. This method combines the perturbation stochastic finite element method with the change-of-variable technique into a united model. To further examine the relationships between the random fields, discretization of the random field parameters, such as the variance function and the scale of fluctuation, is also performed. Accordingly, the reliability index is calculated based on the explicit probability density function of responses with Gaussian or non-Gaussian random fields in any number of elements corresponding to the random field discretization. The numerical examples illustrate the effectiveness of the proposed method for a one-dimensional cantilever reinforced concrete column and a two-dimensional steel plate shear wall. The benefit of this method is that the probability density function of responses can be obtained explicitly without the use simulation techniques. Any type of random variable with any statistical distribution can be incorporated into the calculations, regardless of the restrictions imposed by the type of statistical distribution of random variables. Consequently, this method can be utilized as a suitable guideline for the efficient implementation of stochastic finite element analysis of structures, regardless of the statistical distribution of random variables.

• 한국안전학회지
• /
• 제27권5호
• /
• pp.148-157
• /
• 2012

Reliability-based design optimization (RBDO) problem is usually formulated as an optimization problem to minimize an objective function subjected to probabilistic constraint functions which may include deterministic design variables as well as random variables. The challenging task is that, because the probability models of the random variables are often assumed based on limited data, there exists a possibility of selecting inappropriate distribution models and/or model parameters for the random variables, which can often lead to disastrous consequences. In order to select the most appropriate distribution model from the limited observation data as well as model parameters, this study takes into account a set of possible candidate models for the random variables. The suitability of each model is then investigated by employing performance and risk functions. In this regard, this study enables structural design optimization and fitness assessment of the distribution models of the random variables at the same time. As the first paper of a two-part series, this paper describes a new design method considering probability model uncertainties. The robust performance of the proposed method is presented in Part 2. To demonstrate the effectiveness of the proposed method, an example of ten-bar truss structure is considered. The numerical results show that the proposed method can provide the optimal design variables while guaranteeing the most desirable distribution models for the random variables even in case the limited data are only available.

• 한국레이저가공학회지
• /
• 제15권2호
• /
• pp.11-14
• /
• 2012

In this paper, we have made a proposal concerning the beam shaping mask(BSM) using random-array slits to control intensity distribution profile of laser beam and demonstrated its proprieties experimentally. When a lot of slits are set out irregularly, diffraction patterns of light does not appear but granularity patterns as a bundle of fibers appear. Intensity distribution profile is controlled by densities distribution of circular slits arrayed randomly because the number of slits and its area means amount of light energy through BSM. Namely as the number of slits in high intensity area is increased and that in low intensity area decreased, amount of light energy is same over all local parts. So gaussian intensity distribution could be changed to flat-top.

• 한국수학사학회지
• /
• 제35권6호
• /
• pp.149-170
• /
• 2022

This study discusses in terms of historical genesis whether it is reasonable for Bayes to introduce a prior uniform distribution. In this study, we try to analyze the way he dealt with postulates, lemmas, and propositions in Bayes' essay and to understand its characteristics. The results of the study show that Bayes used random variables for two parameters and that the two random variables were converted to each other through cumulative distribution. Furthermore, it is revealed that the introduction of prior uniform distribution can be justified by this way.

• 한국지반공학회논문집
• /
• 제24권1호
• /
• pp.119-130
• /
• 2008

얕은기초 설계시 이용되는 지반의 물리적 공학적 설계변수들은 고유변동성(inherent variability) 및 측정 오차(measurement error) 등과 같은 여러 가지 요인으로 인하여 불확실성이 필연적으로 내포되어 있다. 본 논문에서는 얕은기초 설계시 기존의 결정론적 방법에서 고려하지 못하는 지반 불확실성 등을 포함한 설계 파라미터의 분산을 고려할 수 있는 확률론적 방법의 신뢰성 설계 사례를 제시하였다. 극한지지력 산정시 확률변수(random variable)인 단위중량, 점착력 및 내부마찰각 그리고 침하량 산정시 탄성계수에 대하여 국내 지반에 대한 적정 확률분포 형태 및 통계적 특성치를 결정하였다. 각 확률변수별로 채택된 분포를 적용하여 지지력과 침하량에 관한 신뢰지수와 파괴확률을 결정하였으며, 목표 신뢰지수 또는 확률에 대한 기초폭을 결정하였다. 얕은기초의 신뢰성 설계에 있어서 정규분포의 일괄적 적용보다는 각 확률변수에 해당하는 적합한 분포형태를 적용, 분석하는 것이 바람직한 것으로 나타났다.

• Journal of the Korean Statistical Society
• /
• 제25권4호
• /
• pp.529-544
• /
• 1996

This paper deals with the problem of estimating the autoregressive random coefficient of a first-order random coefficient autoregressive time series model applied to panel data of time series. The autoregressive random coefficients across individual units are assumed to be a random sample from a truncated normal distribution with the space (-1, 1) for stationarity. The estimates of random coefficients are obtained by an empirical Bayes procedure using the estimates of model parameters. Also, a Monte Carlo study is conducted to support the estimation procedure proposed in this paper. Finally, we apply our results to the economic panel data in Liu and Tiao(1980).

• 제어로봇시스템학회논문지
• /
• 제20권8호
• /
• pp.854-867
• /
• 2014

This paper deals with the performance comparison of a PSO algorithm inspired in the process of simulating the behavior pattern of the organisms. The PSO algorithm finds the optimal solution (fitness value) of the objective function based on a stochastic process. Generally, the stochastic process, a random function, is used with the expression related to the velocity included in the PSO algorithm. In this case, the random function of the normal distribution (Gaussian) or uniform distribution are mainly used as the random function in a PSO algorithm. However, in this paper, because the probability distribution which is various with 2 shape parameters can be expressed, the performance comparison of a PSO algorithm using the beta probability distribution function, that is a random function which has a high degree of freedom, is introduced. For performance comparison, 3 functions (Rastrigin, Rosenbrock, Schwefel) were selected among the benchmark Set. And the convergence property was compared and analyzed using PSO-FIW to find the optimal solution.

• 대한수학회논문집
• /
• 제22권3호
• /
• pp.441-452
• /
• 2007

The exact distributions of X + Y, XY and X/(X + Y) are derived when X and Y are independent generalized Planck random variables.

• 대한수학회보
• /
• 제45권2호
• /
• pp.339-353
• /
• 2008

The distributions of products and ratios of random variables are of interest in many areas of the sciences. In this paper, the exact distributions of the product |XY| and the ratio |X/Y| are derived when X and Y are independent Pearson type VII random variables.