• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1161-1168
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• 2011

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.107.1-107.1
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• 2011

Density Probability Distribution Functions (PDFs) are a classic statistical way to study properties of Interstellar Medium (ISM) turbulence. In our three-dimensional MHD simulations, density PDFs of the position-position velocity (PPV) spaces are close to a log-normal distribution. the PDF widths depend on the plasma parameters such as magnetic strength and sonic Mach number. Futhermore, we compare these simulations results to Galactic molecular clouds observed by Jackson et. al (2006). By fitting of the velocity dispersion in the spectral line observation, volume density PDFs of the defined molecular clouds indicate that the sound speeds of the turbulences seem to have a few times larger than the simulation results. In order to understand the inconsistency with general characteristics of turbulence, we consider other simulations inducing the turbulent flow randomly at small driving scales. We find that the density PDF width decreases at more smaller driving scale. Finally, the simulations suggest that sources of ISM turbulence in Galactic molecular clouds can be important on small scales.

• International conference on construction engineering and project management
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• 2011.02a
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• pp.395-398
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• 2011

This paper introduces stochastic cash-flow modeling integrated with simulation based scheduling. The system makes use of CPM schedule data exported from commercial scheduling software, computes the best fit probability distribution functions (PDFs) of historical activity durations, assigns the PDFs identified to respective activities, simulates the schedule network, computes the deterministic and stochastic project cash-flows, plots the corresponding cash flow diagrams, and estimates the best fit PDFs of overdraft and net profit of a project. It analyzes the effect of different distributions of activity durations on the distribution of overdrafts and net profits, and improves reliability compared to deterministic cash flow analysis.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.9 no.5
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• pp.163-168
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• 2009

Most image segmentation methods are to represent observed feature vectors at each pixel, which are assumed as appropriated probability models. These models can be used by statistical estimating or likelihood clustering algorithms of feature vectors. EM algorithms have some calculation problems of maximum likelihood for unknown parameters from incomplete data and maximum value in post probability distribution. First, the performance is dependent upon starting positions and likelihood functions are converged on local maximum values. To solve these problems, we mixed the Gausian function and histogram at all the level values at the image, which are proposed most suitable image segmentation methods. This proposed algoritms are confirmed to classify most edges clearly and variously, which are implemented to MFC programs.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.33 no.6A
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• pp.652-658
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• 2008

In this paper, a new random access scheme is proposed to improve the probability of successful access. In the conventional scheme, a packet is transmitted by a user using one slot and considered successfully transmitted if a collision does not occur. In comparison, a packet of the proposed scheme is transmitted by a user using one or more slots and considered successfully transmitted if there is at least one slot without collision. We evaluate the optimal number of slots selected by users to maximize the probability of successful access when the probability distribution functions for the number of users are given such as Binomial and Poission distribution. From the numerical analysis, it is shown that the proposed scheme performs better than conventional scheme.

• Journal of Korea Water Resources Association
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• v.43 no.9
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• pp.813-822
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• 2010

An important problem in frequency analysis is the estimation of the quantile for a certain return period. In frequency analysis an assumed probability distribution is fitted to the observed sample data to estimate the quantile at the upper tail corresponding to return periods which are usually much larger than the record length. In most cases, the selection of an appropriate probability distribution is based on goodness of fit tests. The goodness of fit test method can be described as a method for examining how well sample data agrees with an assumed probability distribution as its population. However it gives generally equal weight to differences between empirical and theoretical distribution functions corresponding to all the observations. In this study, the modified Anderson-Darling (AD) test statistics are provided using simulation and the power study are performed to compare the efficiency of other goodness of fit tests. The power test results indicate that the modified AD test has better rejection performances than the traditional tests. In addition, the applications to real world data are discussed and shows that the modified AD test may be a powerful test for selecting an appropriate distribution for frequency analysis when extreme cases are considered.

• International Journal of Contents
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• v.2 no.2
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• pp.17-24
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• 2006

The work presented in this paper is divided into two parts. The first part presents finite urn problems which generate truncated negative binomial random variables. Some combinatorial identities that arose from the negative binomial sampling and truncated negative binomial sampling are established. These identities are constructed and serve important roles when we deal with these distributions and their characteristics. Other important results including cumulants and moments of the distributions are given in somewhat simple forms. Second, the distributions of the maximum of two chi-square variables and the distributions of the maximum correlated F-variables are then derived within the negative binomial sampling scheme. Although multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information and deeper insight regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of these distributions. We supplement our findings with exact simple computational methods where no interpolations are involved.

• International Journal of Contents
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• v.3 no.1
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• pp.1-8
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• 2007

The distributions of the minimum correlated F-variable arises in many applied statistical problems including simultaneous analysis of variance (SANOVA), equality of variance, selection and ranking populations, and reliability analysis. In this paper, negative binomial sampling technique is employed to derive the distributions of the minimum of chi-square variables and hence the distributions of the minimum correlated F-variables. The work presented in this paper is divided in two parts. The first part is devoted to develop some combinatorial identities arised from the negative binomial sampling. These identities are constructed and justified to serve important purpose, when we deal with these distributions or their characteristics. Other important results including cumulants and moments of these distributions are also given in somewhat simple forms. Second, the distributions of minimum, chisquare variable and hence the distribution of the minimum correlated F-variables are then derived within the negative binomial sampling framework. Although, multinomial theory applied to order statistics and standard transformation techniques can be used to derive these distributions, the negative binomial sampling approach provides more information regarding the nature of the relationship between the sampling vehicle and the probability distributions of these functions of chi-square variables. We also provide an algorithm to compute the percentage points of the distributions. The computation methods we adopted are exact and no interpolations are involved.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.21 no.48
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• pp.37-52
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• 1998

In many distribution systems important cost reductions and/or service improvements may be achieved by adopting an efficient inventory policy and proper selection of facilities. These efficiency improvements and service enhancements clearly require an integrated approach towards various logistical planning functions. The areas of inventory control and transportation planning need to be closely coordinated. The purpose of this paper is to construct an integrated model that can minimize the total cost of the transportation and inventory systems between multiple origin and destination points, where in origin point i has the supply of commodities and in destination point j requires the commodities. In this case, demands of the destination points are assumed random variables which have a known probability distribution. Using the lot-size reorder-point policy and the safety stock level that minimize total cost we find optimal distribution centers which transport the commodities to the destination points and suggest an optimal inventory policy to the selected distribution center. We also show if a demand greater than one unit will occur at a particular time, we describe the approximate optional replenishment policy from computational results of this lot-size reorder-point policy. This model is formulated as a 0-1 nonlinear integer programming problem. To solve the problem, this paper proposes heuristic computational procedures and a computer program with UNIX C language. In the usefulness review, we show the meaning and validity of the proposed model and exhibit the results of a comparison between our approach and the traditional approach, respectively.

• Journal of Electrical Engineering and Technology
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• v.8 no.3
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• pp.453-463
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• 2013

The probabilistic nature of renewable energy, especially wind energy, increases the needs for new forms of planning and operating with electrical power. This paper presents a novel approach for determining the short-term generation schedule for optimal operations of wind energy-integrated power systems. The proposed probabilistic security-constrained optimal power flow (P-SCOPF) considers dispatch, network, and security constraints in pre- and post-contingency states. The method considers two sources of uncertainty: power demand and wind speed. The power demand is assumed to follow a normal distribution, while the correlated wind speed is modeled by the Weibull distribution. A Monte Carlo simulation is used to choose input variables of power demand and wind speed from their probability distribution functions. Then, P-SCOPF can be applied to the input variables. This approach was tested on a modified IEEE 30-bus system with two wind farms. The results show that the proposed approach provides information on power system economics, security, and environmental parameters to enable better decision-making by system operators.