• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.28 no.6
• /
• pp.685-692
• /
• 2004

A stochastic approach has been presented for superplastic deformation of Ti-6Al-4V alloy, and probability functions are used to model the heterogeneous phase distributions. The experimentally observed spatial correlation functions are developed, and microstructural evolutions together with superplastic deformation behavior have been investigated by means of the two-point and three-point probability functions. The results have shown that the probability varies approximately linearly with separation distance, and deformation enhanced probability changes during the process. The stress-strain behavior with the evolutions of probability function can be correctly predicted by the model. The finite element implementation using Monte Carlo simulation associated with reconstructed microstructures shows that better agreement with experimental data of failure strain on the test specimen.

• Water for future
• /
• v.7 no.2
• /
• pp.107-111
• /
• 1974

Annual runoff in the Nakdong river basin has been analyzed to find the probability functions of best fit to distribution of historical annual runoff. The results obtained are as follows; (1) Log-normal 3-parameter disrtibution is believed as the probability function of best fit to historical distribution (2) Log-normal 3-parameter disrtibution is believed as the best fit probability function among Log-normal dist-ributions. (3) In the test of goodness of fit, $x^2-test$ shows that probability of $x^2-valus$ in Log-normal 3-parameter distribution is nearly more than 90%. But in the Simirnov-Kolmogorov test, hypotheses for the probability distributions cannot be rejected at significance level 5% & 1%. (4) Among 7 gauging stations, Dongchon & Koryung-Bridge's records show lower fitness to the theoretical probability functions than other 5 gauging station's

• Journal of Electrical Engineering and information Science
• /
• v.1 no.1
• /
• pp.151-155
• /
• 1996

This paper derives the two-dimensional probability distribution and density functions of morphological dilation and erosion of a one-dimensional memoryless source and reports numerical results for a uniform source, thus providing methodology for joint distributions for other morphological operations. The joint density functions expressed in closed forms contain the Dirac delta functions due to the joint discontinuity within the dilation and erosion. They also exhibit symmetry between these two morphological density functions of dilated and/or eroded sources, in the computation of other higher moments thereof, and in multidimensional quantization.

• The Korean Journal of Applied Statistics
• /
• v.26 no.5
• /
• pp.759-766
• /
• 2013

The paper examines several classes of probability distributions with heavy tails. An (asymptotic) expression for tail probability needs to be known to understand which class a given probability distribution belongs to. It is usually not easy to get expressions for tail probabilities since most absolutely continuous probability distributions are specified by probability density functions and not by distribution functions. The paper proposes a method to obtain asymptotic expressions for tail probabilities using only probability density functions. Some examples are given to illustrate the proposed method.

• Journal of the Korean Society of Marine Environment & Safety
• /
• v.21 no.3
• /
• pp.253-258
• /
• 2015

The purpose of this study is to find suitable probability distribution function of complex distribution data like multimodal. Normal distribution is broadly used to assume probability distribution function. However, complex distribution data like multimodal are very hard to be estimated by using normal distribution function only, and there might be errors when other distribution functions including normal distribution function are used. In this study, we experimented to find fit probability distribution function in multimodal area, by using AIS(Automatic Identification System) observation data gathered in Mokpo port for a year of 2013. By using chi-squared statistic, gaussian mixture model(GMM) is the fittest model rather than other distribution functions, such as extreme value, generalized extreme value, logistic, and normal distribution. GMM was found to the fit model regard to multimodal data of maritime traffic flow distribution. Probability density function for collision probability and traffic flow distribution will be calculated much precisely in the future.

• Proceedings of the KIEE Conference
• /
• 2002.07b
• /
• pp.1338-1341
• /
• 2002

The Weibull probability density function and the Rayleigh function are compared by analyzing the relations of the capacity factors which are compared the actual wind speed frequency curve with which are modelled 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 shows 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.

• Journal of Industrial Technology
• /
• v.21 no.B
• /
• pp.163-174
• /
• 2001

A dynamic reliability model for analyzing the stability of armor units on rubble-mound breakwater is mathematically developed by using Hudson's formula and definition of single-failure mode. The probability density functions of resistance and loading functions are defined properly, the related parameters to those probability density functions are also estimated straightforwardly by the first-order analysis. It is found that probabilities of failure for the stability of armor units on rubble-mound breakwater are continuously increased as the service periods are elapsed, because of the occurrence of repeated loading of random magnitude by which the resistance may be deteriorated. In particular, the factor of safety is incorporated into the dynamic reliability model in order to evaluate the probability of failure as a function of factor of safety. It may thus be possible to take some informations for optimal design as well as managements and repairs of armor units on rubble-mound breakwater from the dynamic reliability analyses.

• Journal for History of Mathematics
• /
• v.32 no.3
• /
• pp.135-155
• /
• 2019

One of the reasons students have difficulty in studying probability is that they do not understand the meaning of mathematical terms precisely. One such term is a continuous random variable. Students tend not to think of the accurate definition of continuous random variables but to understand the definition of continuity of functions and the meaning of continuity in probability as equal. In this study, we try to explore the degree of pre-service teachers' understanding on the concept of continuation of functions and continuous random variables. To do this, the questionnaire items related to continuous random variables and continuity of functions were developed by experts and examined by pre-service teachers. Based on this, we make suggestions on implications for teaching and learning about continuous random variables.

• Journal of the military operations research society of Korea
• /
• v.25 no.1
• /
• pp.160-168
• /
• 1999

This research focussed on developing a hit probability model for polygonal target to increase the survivability of weapon systems by its shape design. First, we defined the delivery errors and derived functions for these errors based on the assumption of bivariate normal distribution, and the derived functions for probability of shot hitting of various shapes of polygonal target. Also, we developed computer program for computation of the probability of hitting a general n-sided polygon and we have shown a sample run output. The model could be used to improve the survivability from design phase by designing optimal polygonal shape of weapon system.

• ETRI Journal
• /
• v.32 no.6
• /
• 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.