• International Journal of Advanced Culture Technology
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• v.7 no.4
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• pp.268-273
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• 2019

The apparent soil resistivity is used for estimating multilayer soil parameters, such as, layer's depth and soil resistivity. The soil parameters are estimated by continuously revising those parameters until the error between the measured and calculated apparent soil resistivity reaches to allowable level. The equation for calculating the apparent soil resistivity is complicated and time consumed, because it is composed of an infinite integral which includes a zero order Bessel's function of the first kind. In this paper, a fast algorithm for calculating the apparent soil resistivity of horizontal multilayer earth structure is proposed using exponential sampling method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.3
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• pp.475-485
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• 2017

This paper develops a conversion function and method transforming from daily peak load curve used $LOLE_D$ [days/year] to hourly load curve used $LOLE_H$[hours/year]and describes relationship between $LOLE_D$ [days/year] and $LOLE_H$ [hours/year]. The indices can not only be transformed just arithmetically but also have different characteristics physically because of using their different load curves. The conversion function is formulated as variables of capacity and forced outage rate of generator, hourly load daily load factor and daily peak load yearly load factor, etc. Therefore, the conversion function (${\gamma}={\varphi}$(.)) can not be simple. In this study, therefore, the function is formulated as linear times of separated two functions. One is an exponential formed conversion function of daily load factor. Another is formulated with an exponential typed conversion function of daily peak load yearly load factor. Futhermore, this paper presents algorithm and flow chart for transforming from $LOLE_D$[days/year] to $LOLE_H$[hours/year]. The proposed conversion function is applied to sample system and actual KPS(Korea Power System) in 2015. The exponent coefficients of the conversion functions are assessed using proposed method. Finally, assessment errors using conversion function for case studies of sample system and actual system are evaluated to certify the firstly proposed method.

• Communications of the Korean Mathematical Society
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• v.26 no.4
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• pp.709-720
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• 2011

We obtain special type of differential equations which their solution are random variable with known continuous density function. Stochastic differential equations (SDE) of continuous distributions are determined by the Fokker-Planck theorem. We approximate solution of differential equation with numerical methods such as: the Euler-Maruyama and ten stages explicit Runge-Kutta method, and analysis error prediction statistically. Numerical results, show the performance of the Rung-Kutta method with respect to the Euler-Maruyama. The exponential two parameters, exponential, normal, uniform, beta, gamma and Parreto distributions are considered in this paper.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.30 no.7 s.250
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• pp.787-793
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• 2006

Recently kriging model has been widely used in the DACE (Design and Analysis of Computer Experiment) because of prominent predictability of nonlinear response. Since DACE has no random or measurement errors contrast to physical experiment, space filling experimental design that distributes uniformly design points over whole design space should be employed as a sampling method. In this paper, we examine the maximum entropy experimental design that reveals the space filling strategy in which defines the maximum entropy based on Gaussian or exponential. The influence of these two correlation functions on space filling design and their model parameters are investigated. Based on the exploration of numerous numerical tests, enhanced maximum entropy design based on exponential correlation function is suggested.

• Communications for Statistical Applications and Methods
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• v.20 no.5
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• pp.387-394
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• 2013

In this paper, we develop the noninformative priors for the ratio of the scale parameters in the inverted exponential distributions. The first and second order matching priors, the reference prior and Jeffreys prior are developed. It turns out that the second order matching prior matches the alternative coverage probabilities, is a cumulative distribution function matching prior and is a highest posterior density matching prior. In addition, the reference prior and Jeffreys' prior are the second order matching prior. We show that the proposed reference prior matches the target coverage probabilities in a frequentist sense through a simulation study as well as provide an example based on real data is given.

• Journal of the Korean Mathematical Society
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• v.49 no.3
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• pp.537-547
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• 2012

In this paper, we define a $p$, $q$-difference operator and obtain an explicit formula which is used to express the $p$, $q$-analogue of the unified generalization of Stirling numbers and its exponential generating function in terms of the $p$, $q$-difference operator. Explicit formulas for the non-central $q$-Stirling numbers of the second kind and non-central $q$-Lah numbers are derived using the new $q$-analogue of Newton's interpolation formula. Moreover, a $p$, $q$-analogue of Newton's interpolation formula is established.

• Fire Science and Engineering
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• v.33 no.6
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• pp.20-27
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• 2019

In this study, a new function with higher accuracy for fire heat release rate prediction was developed. The 'αt²' curve, which is the major exponential function currently used for fire engineering calculations, must be improved to minimize the prediction gap that causes fire system engineering inefficiency and lower cost-effectiveness. The newly developed prediction function was designed to cover the initial fire stage that features rapid growth based on logistic function theory, which has a more logical background and graphical similarity compared to conventional exponential function methods for 'αt²'. The new function developed in this study showed apparently higher prediction accuracy over wider range of fire growth durations. With the progress of fire growth pattern studies, the results presented herein will contribute towards more effective fire protection engineering.

• Communications for Statistical Applications and Methods
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• v.7 no.2
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• pp.371-383
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• 2000

Lindsay (1994) and Basu et al (1997) show that another density-based distance called the negative exponential disparity (NED) is an excellent competitor to the Hellinger distance (HD) in generating an asymptotically fully efficient and robust estimator. Bhattacharya and Basu (1996) consider estimation of the locations of several normal populations when an order relation between them is known to be true. They empirically show that the robust HD based weighted likelihood estimators compare favorably with the M-estimators based on Huber's $\psi$ function, the Gastworth estimator, and the trimmed mean estimator. In this paper we investigate the performance of the weighted likelihood estimator based on the NED as a robust alternative relative to that based on the HD. The NED based estimator is found to be quite competitive in the settings considered by Bhattacharya and Basu.

• 한국데이터정보과학회:학술대회논문집
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• 2005.10a
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• pp.13-26
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• 2005

In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponential distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples. We also obtain the approximate maximum likelihood estimator (AMLE) of the reliability function by using the proposed estimators. And then we compare the proposed estimators in the sense of the mean squared error.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.2
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• pp.325-328
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• 2022

A convolutional neural network(CNN) is widely used in the computer vision tasks, but its computing power requirement needs a design of a special circuit. Most of the computations in a CNN can be implemented efficiently in a digital circuit, but the SoftMax layer has operations unsuitable for circuit implementation, which are exponential and logarithmic functions. This paper proposes a new method to integrate the exponential and logarithmic tables of the conventional circuits into a single table. The proposed structure accesses a look-up table (LUT) only with a few maximum values, and the LUT has the result value directly. Our proposed method significantly reduces the space complexity of the SoftMax layer circuit implementation. But our resulting circuit is comparable to the original baseline with small degradation in precision.