• Communications for Statistical Applications and Methods
• /
• v.21 no.2
• /
• pp.125-134
• /
• 2014

Kullback-Leibler (KL) information is a measure of discrepancy between two probability density functions. However, several nonparametric density function estimators have been considered in estimating KL information because KL information is not well-defined on the empirical distribution function. In this paper, we consider the KL information of the equilibrium distribution function, which is well defined on the empirical distribution function (EDF), and propose an EDF-based goodness of fit test statistic. We evaluate the performance of the proposed test statistic for an exponential distribution with Monte Carlo simulation. We also extend the discussion to the censored case.

• Journal of Korean Society of Industrial and Systems Engineering
• /
• v.20 no.43
• /
• pp.47-57
• /
• 1997

As a general index in surface quality of machined products, surface roughness is to measure worker's skill level, a ground product quality and machining accuracy, etc. The surface roughness is defined by a function of rotational speed and radius of a grinding wheel, distances of active grains composed of the wheel, and feed of a grinder's worktable. To predict surface roughness in horizontal surface grinding operations, probability distributions were used. Probability distribution functions(p.d.f.) of surface roughness were found as results when the size of active grains(=the radius of a grinding wheel) is given as uniform, exponential distribution, and the distance between active grains follows the distributions of uniform, exponential. For each pdf case, probabilistic features of surface roughness were also analyzed and presented. This study is a substantial step for determining mathematically the surface roughness instead of using empirical approaches. More works should be presented to develop a general model by which an accurate roughness value can be obtained in horizontal surface grinding operations.

• Kyungpook Mathematical Journal
• /
• v.64 no.1
• /
• pp.95-111
• /
• 2024

The filled function method is useful in solving unconstrained global optimization problems. However, depending on the type of function, and parameters used, there are limitations that cause difficultiies in implemenations. Exponential and logarithmic functions lead to the overflow effect, requiring iterative adjustment of the parameters. This paper proposes a polynomial-filled function that has a general form, is non-exponential, nonlogarithmic, non-parameteric, and continuously differentiable. With this newly proposed filled function, the aforementioned shortcomings of the filled function method can be overcome. To confirm the superiority of the proposed filled function algorithm, we apply it to a set of unconstrained global optimization problems. The data derived by numerical implementation shows that the proposed filled function can be used as an alternative algorithm when solving unconstrained global optimization problems.

• Communications for Statistical Applications and Methods
• /
• v.31 no.4
• /
• pp.427-440
• /
• 2024

The problem addressed is that of sequentially estimating the difference between the means of two populations with respect to the squared error loss, where each population distribution is a member of the one-parameter exponential family. A Bayesian approach is adopted in which the population means are estimated by the posterior means at each stage of the sampling process and the prior distributions are not specified but have twice continuously differentiable density functions. The main result determines an asymptotic second-order lower bound, as t → ∞, for the Bayes risk of a sequential procedure that takes M observations from the first population and t - M from the second population, where M is determined according to a sequential design, and t denotes the total number of observations sampled from both populations.

• Wind and Structures
• /
• v.21 no.2
• /
• pp.119-158
• /
• 2015

The characteristics of the coherence functions of X axial, Y axial, and RZ axial (i.e., body axis) wind forces on the Shanghai World Trade Centre - a 492 m super-tall building with section varying along height are studied via a synchronous multi-pressure measurement of the rigid model in wind tunnel simulating of the turbulent, and the corresponding mathematical expressions are proposed there from. The investigations show that the mathematical expressions of coherence functions in across-wind and torsional-wind directions can be constructed by superimposition of a modified exponential decay function and a peak function caused by turbulent flow and vortex shedding respectively, while that in along-wind direction need only be constructed by the former, similar to that of wind speed. Moreover, an inductive analysis method is proposed to summarize the fitted parameters of the wind force coherence functions of every two measurement levels of altitudes. The comparisons of the first three order generalized force spectra show that the proposed mathematical expressions accord with the experimental results well. Later, the influences of coherence functions on wind-induced dynamic responses are analyzed in detail based on the proposed mathematical expressions and the frequency-domain method of random vibration theory.

• Journal of Korean Society of Transportation
• /
• v.27 no.1
• /
• pp.157-167
• /
• 2009

This study deals with the turn penalty functions in the urban transportation demand forecasting. The objectives are to develop the penalty functions of left-turn traffic in the case of signalized intersections, and to analyze the applicability of the functions to the traffic assignment models. This is based on the background that the existing models can not effectively account for the delays of left-turn traffic which is bigger than that of through traffic. In pursuing the above, this study gives particular attention to developing the penalty functions based on the degrees of saturation by simulation results of Transyt-7F, and analyzing the applicability of the functions by the case study of Cheongju. The major findings are the followings. First, two penalty functions developed according to the degrees of saturation, are evaluated to be all statistically significant. Second, the results that the above functions apply to the Cheongju network, are analyzed to be converging, though the iteration numbers increase. Third, the link volumes forecasted by turn penalty functions are evaluated to be better fitted to the observed data than those by the existing models. Finally, the differences of traffic volumes assigned by two functions, which are exponential and divided forms, are analyzed to be very small.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.15 no.3
• /
• pp.1724-1733
• /
• 2014

This paper presents a pattern recognition analysis of two spirals problem and optimization of Cascade Correlation learning algorithm using in combination with a non-monotone function as CosExp(cosine-modulated symmetric exponential function) and a monotone function as sigmoid function. In addition, the algorithm's optimization is attempted. By using genetic algorithms the optimization of the algorithm will attempt. In the first experiment, by using CosExp activation function for candidate neurons of the learning algorithm is analyzed the recognized pattern in input space of the two spirals problem. In the second experiment, CosExp function for output neurons is used. In the third experiment, the sigmoid activation functions with various parameters for candidate neurons in 8 pools and CosExp function for output neurons are used. In the fourth experiment, the parameters are composed of 8 pools and displacement of the sigmoid function to determine the value of the three parameters is obtained using genetic algorithms. The parameter values applied to the sigmoid activation functions for candidate neurons are used. To evaluate the performance of these algorithms, each step of the training input pattern classification shows the shape of the two spirals. In the optimizing process, the number of hidden neurons was reduced from 28 to15, and finally the learning algorithm with 12 hidden neurons was optimized.

• The Korean Journal of Nuclear Medicine
• /
• v.39 no.4
• /
• pp.257-262
• /
• 2005

Purpose: Gastric emptying scan (GES) is usually acquired up to 2 hours. Our study investigated whether a fraction of meal-retention in the stomach at 120 minutes (FR120) was predicted from the data measured for 90 minutes by using non-linear curve fitting. We aimed at saving the delayed imaging by utilizing mathematical models. Materials and Methods: Ninety-six patients underwent GES immediately after taking a boiled egg with 74 MBq (2 mCi) Tc-99m DTPA. The patients were divided into Group I ($T_{1/2}\;{\leq}90\;min$) and Group II ($90\;min). Group I (n=51) had 21 men and 30 women, and Group II (n=45) 15 men and 30 women. There was no significant difference in age and sex between the two groups. Simple exponential, power exponential, and modified power exponential curves were acquired from the measured fraction of meal-retention at each time (0, 15, 30, 45, 60, 75, and 90 min) by non-linear curve fitting ($MATLAB^{\circledR}$ 5.3) and another simple exponential fitting was performed on the fractions at late times (60, 75, and 90 min). A predicted FR120 was calculated from the acquired functional formulas. A correlation coefficient between the measured FR120 and the predicted FR120 was computed ($MedCalc^{\circledR}$ 6.0). Results: Correlation coefficients(r) between the measured FR120 and the predicted FR120 of each mathematical functions were as follows: simple exponential function (Group I: 0.8558, Group II: 0.5982, p<0.0001), power exponential function (Group I: 0.8755, Group II: 0.6008, p<0.0001), modified power exponential function (Group I: 0.8892, Group II: 0.5882, p<0.0001), and simple exponential function at the late times(Group I: 0.9085, Group II: 0.6832, p<0.0001). In all the fitting models, the predicted FR120 were significantly correlated with the measured FR120 in Group I but not in Group II. There was no statistically significant difference in correlation among the 4 mathematical models. Conclusion: In the cases with $T_{1/2}\;{\leq}90\;min$, the predicted FR120 is significantly correlated with the measured FR120. Therefore, FR120 can be predicted from the data measured for 90 minutes by using non-linear curve fitting, saving the delayed imaging after 90 minutes when $T_{1/2}\;{\leq}90\;min$ is ascertained.

• Bulletin of the Korean Mathematical Society
• /
• v.34 no.3
• /
• pp.371-383
• /
• 1997

In recent years M. Pinto introduced the notion of h-stability. He extended the study of exponential stability to a variety of reasonable systems called h-systems. We investigate h-stability for the nonlinear differential systems using the notions of $t_\infty$-similarity and Liapunov functions.

• Journal of the Korean Statistical Society
• /
• v.15 no.2
• /
• pp.87-96
• /
• 1986

Sequential estimation of parameters in a compound Poisson process whose jump sizes are one-parameter exponential class random variables is discussed. Cramer-Rao type information inequality is used as an efficiency cirterion. Unbiased estimators for certain parametric functions whose variance attain the lower bound are all characterized with the corresponding sampling plans.