• East Asian mathematical journal
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• v.39 no.5
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• pp.537-547
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• 2023

In this paper, we introduce the optimal approximation by a Gaussian function for a probability density function. We show that the approximation can be obtained by solving a non-linear system of parameters of Gaussian function. Then, to understand the non-normality of the empirical distributions observed in financial markets, we consider the nearly Gaussian function that consists of an optimally approximated Gaussian function and a small periodically oscillating density function. We show that, depending on the parameters of the oscillation, the nearly Gaussian functions can have fairly thick heavy tails.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
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• v.5B no.3
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• pp.258-261
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• 2005

The Preisach model needs a distribution function or Everett function to simulate the hysteresis phenomena. To obtain these functions, many experimental data obtained from the first order transition curves are usually required. In this paper, a simple procedure to determine the Preisach density function using the Gaussian distribution function and genetic algorithm is proposed. The Preisach density function for the interaction field axis is known to have Gaussian distribution. To determine the density and distribution, genetic algorithm is adopted to decide the Gaussian parameters. With this method, just basic data like the initial magnetization curve or saturation curves are enough to get the agreeable density function. The results are compared with experimental data and we got good agreements comparing the simulation results with the experiment ones.

• Composites Research
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• v.29 no.5
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• pp.299-305
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• 2016

This paper presents a method to detect the fiber property variation of laminated CFRP plates using the bivariate Gaussian distribution function. Five unknown parameters are considered to determine the fiber damage distribution, which is a modified form of the bivariate Gaussian distribution function. To solve the inverse problem using the combined computational method, this study uses several natural frequencies and mode shapes in a structure as the measured data. The numerical examples show that the proposed technique is a feasible and practical method which can prove the location of a damaged region as well as inspect the distribution of deteriorated stiffness of CFRP plates for different fiber angles and layup sequences.

• Journal of information and communication convergence engineering
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• v.10 no.2
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• pp.200-204
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• 2012

This study has presented the analysis of breakdown voltage for a double-gate metal-oxide semiconductor field-effect transistor (MOSFET) based on the doping distribution of the Gaussian function. The double-gate MOSFET is a next generation transistor that shrinks the short channel effects of the nano-scaled CMOSFET. The degradation of breakdown voltage is a highly important short channel effect with threshold voltage roll-off and an increase in subthreshold swings. The analytical potential distribution derived from Poisson's equation and the Fulop's avalanche breakdown condition have been used to calculate the breakdown voltage of a double-gate MOSFET for the shape of the Gaussian doping distribution. This analytical potential model is in good agreement with the numerical model. Using this model, the breakdown voltage has been analyzed for channel length and doping concentration with parameters such as projected range and standard projected deviation of Gaussian function. As a result, since the breakdown voltage is greatly changed for the shape of the Gaussian function, the channel doping distribution of a double-gate MOSFET has to be carefully designed.

• Proceedings of the IEEK Conference
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• 2002.07a
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• pp.26-29
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• 2002

Radial Basis Function (RBF) networks is known as efficient method in classification problems and function approximation. The basis function of RBF networks is usual adopted normal distribution like the Gaussian function. The output of the Gaussian function has the maximum at the center and decrease as increase the distance from the center. For learning of neural network, the method treating the limited area of input space is sometimes more useful than the method treating the whole of input space. The q-normal distribution is the set of probability density function include the Gaussian function. In this paper, we introduce the RBF networks with the basis function of q-normal distribution and actually approximate a function using the RBF networks.

• ETRI Journal
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• v.32 no.1
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• pp.145-147
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• 2010

In this letter, we present a new approximation for the twodimensional (2-D) Gaussian Q-function. The result is represented by only the one-dimensional (1-D) Gaussian Q-function. Unlike the previous 1-D Gaussian-type approximation, the presented approximation can be applied to compute the 2-D Gaussian Q-function with large correlations.

• Wind and Structures
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• v.31 no.6
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• pp.549-560
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• 2020

Methods for stochastic simulation of non-Gaussian wind pressure have increasingly addressed the efficiency and accuracy contents to offer an accurate description of the extreme value estimation of the long-span and high-rise structures. This paper presents a linear prediction and z-transform (LPZ) based Cumulative distribution function (CDF) mapping algorithm for the simulation of multivariate non-Gaussian fluctuating wind pressure. The new algorithm generates realizations of non-Gaussian with prescribed marginal probability distribution function (PDF) and prescribed spectral density function (PSD). The inverse linear prediction and z-transform function (ILPZ) is deduced. LPZ is improved and applied to non-Gaussian wind pressure simulation for the first time. The new algorithm is demonstrated to be efficient, flexible, and more accurate in comparison with the FFT-based method and Hermite polynomial model method in two examples for transverse softening and longitudinal hardening non-Gaussian wind pressures.

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

• Journal of the Korea Institute of Information and Communication Engineering
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• v.18 no.5
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• pp.1143-1148
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• 2014

This paper has analyzed the change of subthreshold swing for doping distribution function of asymmetric double gate(DG) MOSFET. The basic factors to determine the characteristics of DGMOSFET are dimensions of channel, i.e. channel length and channel thickness, and doping distribution function. The doping distributions are determined by ion implantation used for channel doping, and follow Gaussian distribution function. Gaussian function has been used as carrier distribution in solving the Poisson's equation. Since the Gaussian function is exactly not symmetric for top and bottome gates, the subthreshold swings are greatly changed for channel length and thickness, and the voltages of top and bottom gates for asymmetric double gate MOSFET. The deviation of subthreshold swings has been investigated for parameters of Gaussian distribution function such as projected range and standard projected deviation in this paper. As a result, we know the subthreshold swing is greatly changed for doping profiles and bias voltage.

• ETRI Journal
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• v.33 no.6
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• pp.949-952
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• 2011

In this letter, a simplified suboptimum receiver based on soft-limiting for the detection of binary antipodal signals in non-Gaussian noise modeled as a generalized normal-Laplace (GNL) distribution combined with Gaussian noise is presented. The suboptimum receiver has low computational complexity. Furthermore, when the number of diversity branches is small, its performance is very close to that of the Neyman-Pearson optimum receiver based on the probability density function obtained by the Fourier inversion of the characteristic function of the GNL-plus-Gaussian distribution.