• Journal of the Korean Data and Information Science Society
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• 제26권3호
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• pp.763-772
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• 2015

In this paper, we develop the noninformative priors for the product of different powers of k means in the exponential distribution. We developed the first and second order matching priors. It turns out that the second order matching prior matches the alternative coverage probabilities, and is the highest posterior density matching prior. Also we revealed that the derived reference prior is the second order matching prior, and Jeffreys' prior and reference prior are the same. We showed that the proposed reference prior matches very well the target coverage probabilities in a frequentist sense through simulation study, and an example based on real data is given.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1993년도 Fifth International Fuzzy Systems Association World Congress 93
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• pp.1281-1284
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• 1993

By the exponential representation form (EF) for fuzzy logic, any fuzzy value a (in fuzzy valued logic or fuzzy linguistic valued logic) can be represented as Bc, where B is called the truth base and C the confidence exponent. This paper will propose the basic concepts of this form and discuss its interesting properties. By using a different truth base, the exponential form can be used to represent the positive and the negative logic in fuzzy valued logic as well as in fuzzy linguistic valued logic. Some Simple application examples of EF for approximate reasoning are also illustrated in this paper.

• 한국정보통신학회논문지
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• 제26권2호
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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.

• Communications for Statistical Applications and Methods
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• 제21권5호
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• pp.461-469
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• 2014

Characteristic functions play an important role in probability and statistics; however, a rigorous derivation of these functions requires contour integration, which is unfamiliar to most statistics students. Without resorting to contour integration, Datta and Ghosh (2007) derived the characteristic functions of normal, Cauchy, and double exponential distributions. Here, we derive the characteristic functions of t, truncated normal, skew-normal, and skew-t distributions. The characteristic functions of normal, cauchy distributions are obtained as a byproduct. The derivations are straightforward and can be presented in statistics masters theory classes.

• 한국물환경학회지
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• 제24권3호
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• pp.345-353
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• 2008

In order to design storage-based non-point source management facilities, the aspect of statistical features of the entire precipitation time series should be considered since non-point source pollutions are delivered by continuous rainfall runoffs. The 3-parameter mixed exponential probability density function instead of traditional single-parameter exponential probability density function is applied to represent the probabilistic features of long-term precipitation time series and model urban stormwater runoff. Finally, probability density functions of water quality control basin overflow are derived under two extreme intial conditions. The 31-year continuous precipitation time series recorded in Busan are analyzed to show that the 3-parameter mixed exponential probability density function gives better resolution.

• Journal of applied mathematics & informatics
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• 제2권2호
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• pp.13-20
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• 1995

The goal of this paper is to show that the linear approxi-mation in evaluation of functions may be effectively replaced by the ex-ponential approximation formulas obtained by numerical quadratures and in the instance the relative errors can be estimated without know-ing the true values.

• 호남수학학술지
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• 제41권4호
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• pp.863-870
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• 2019

In this paper, we obtain the enumeration results on the number of linear extensions of diamond posets. We find the recurrence relations and exponential generating functions for the number of linear extensions of diamond posets. We also get some results for the volume of graph polytope associated with bipartite graphs which are underlying graphs of diamond posets.

• Journal of applied mathematics & informatics
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• 제36권5_6호
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• pp.505-519
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• 2018

In this paper we define a (p, q)-Laplace transform. By using this definition, we obtain many properties including the linearity, scaling, translation, transform of derivatives, derivative of transforms, transform of integrals and so on. Finally, we solve the differential equation using the (p, q)-Laplace transform.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 2000년도 제15차 학술회의논문집
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• pp.315-315
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• 2000

In this paper, we perform the time series prediction using the SVM(Support Vector Machine). We make use of two different loss functions and two different kernel functions; i) Quadratic and $\varepsilon$-insensitive loss function are used; ii) GRBF(Gaussian Radial Basis Function) and ERBF(Exponential Radial Basis Function) are used. Mackey-Glass time series are used for prediction. For both cases, we compare the results by the SVM to those by ANN(Artificial Neural Network) and show the better performance by SVM than that by ANN.

• 호남수학학술지
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• 제41권1호
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• pp.163-174
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• 2019

The veritable pursuit of this exegesis is to exhibit integrals affined with the Bessel-Struve kernel function, which are explicitly inscribed in terms of generalized (Wright) hypergeometric function and also the product of generalized (Wright) hypergeometric function with sum of two confluent hypergeometric functions. Somewhat integrals involving exponential functions, modified Bessel functions and Struve functions of order zero and one are also obtained as special cases of our chief results.