• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.123-137
• /
• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.15 no.11
• /
• pp.955-961
• /
• 1990

Test statistics are obtained for detection of weak signals in signal-dependent noise using rank statistics. A generalized model is used in this paper in order to consider non-additivenoise as well as purely-additive noise. Locally optimum rank detectors for the model are shown to have similarity to locally optimum detectors and to be generalizations of these for the purely-additive noise model. A similar result is obtained for multi-input cases.

• Journal of Institute of Control, Robotics and Systems
• /
• v.14 no.8
• /
• pp.727-732
• /
• 2008

In this paper, the state-space representation of generalized complimentary filter is proposed. Complementary filter has the suitable structure to merge information from sensors whose frequency regions are complementary. First, the basic concept and structure of complementary filter is introduced. And then the structure of the generalized filter and its state-space representation are proposed. The state-space representation of complementary filter is able to design the complementary filter by applying modern filtering techniques like Kalman filter and $H_{\infty}$ filter. To show the usability of the proposed state-space representation, the design of Inertial Navigation System(INS) vertical channel damping loop using Global Positioning System(GPS) is described. The proposed GPS/INS damping loop lends the structure of Baro/INS(Barometer/INS) vertical channel damping loop that is an application of complementary filter. GPS altitude error has the non-stationary statistics although GPS offers navigation information which is insensitive to time and place. Therefore, $H_{\infty}$ filtering technique is selected for adding robustness to the loop. First, the state-space representation of GPS/INS damping loop is acquired. And next the weighted $H_{\infty}$ norm proposed in order to suitably consider characteristics of sensor errors is used for getting filter gains. Simulation results show that the proposed filter provides better performance than the conventional vertical channel loop design schemes even when error statistics are unknown.

• The Journal of the Acoustical Society of Korea
• /
• v.24 no.4
• /
• pp.224-229
• /
• 2005

In this paper, we Propose a novel cepstrum normalization method which normalizes the probability density function (pdf) of cepstrum for robust speech recognition in additive noise environments. While the conventional methods normalize the first- and/or second-order statistics such as the mean and/or variance of the cepstrum. the proposed method fully normalizes the statistics of cepstrum by making the pdfs of clean and noisy cepstrum identical to each other For the target Pdf, the generalized Gaussian distribution is selected to consider various densities. In recognition phase, we devise a table lookup method to save computational costs. From the speaker-independent isolated-word recognition experiments, we show that the Proposed method gives improved Performance compared with that of the conventional methods, especially in heavy noise environments.

• The Korean Journal of Applied Statistics
• /
• v.18 no.1
• /
• pp.43-56
• /
• 2005

In this study, a robust estimation method for the first-order autocorrelation coefficient in the time series model following AR(l) process with additive outlier(AO) is investigated. We propose the L-type trimmed least squares estimation method using the preliminary estimator (PE) suggested by Rupport and Carroll (1980) in multiple regression model. In addition, using Mallows' weight function in order to down-weight the outlier of X-axis, the bounded-influence PE (BIPE) estimator is obtained and the mean squared error (MSE) performance of various estimators for autocorrelation coefficient are compared using Monte Carlo experiments. From the results of Monte-Carlo study, the efficiency of BIPE(LAD) estimator using the generalized-LAD to preliminary estimator performs well relative to other estimators.

• The Bulletin of The Korean Astronomical Society
• /
• v.46 no.2
• /
• pp.72.3-73
• /
• 2021

Baryon Acoustic Oscillations (BAO) are caused by acoustic density waves in the early universe and act as a standard ruler in the clustering pattern of galaxies in the late Universe. Measuring the BAO feature in the 2-point correlation function of a sample of galaxies allows us to estimate cosmological distances to the galaxies mean redshift, , which is important for testing and constraining the cosmology model. The BAO feature is also expected to appear in the higher order statistics. In this work we measure the generalized spatial N-point point correlation functions up to 4th order. We made measurements of the 2, 3, and 4-point correlation functions in the SDSS-III DR12 CMASS data, comprising of 777,202 galaxies. The errors and covariances matrices were estimated from 500 mock catalogues. We created a theoretical model for these statistics by measuring the N-point functions in halo catalogues produced by the approximate Lagrangian perturbation theory based simulation code, PINOCCHIO. We created simulations using initial conditions with and without the BAO feature. We find that the BAO is detected to high significance up to the 4-point correlation function.

• East Asian mathematical journal
• /
• v.17 no.1
• /
• pp.135-146
• /
• 2001

Several families of infinite series were summed recently by means of certain operators of fractional calculus(that is, calculus of derivatives and integrals of any real or complex order). In the present sequel to this recent work, it is shown that much more general classes of infinite sums can be evaluated without using fractional calculus. Some other related results are also considered.

• Honam Mathematical Journal
• /
• v.39 no.3
• /
• pp.401-416
• /
• 2017

Fractional kinetic equations are investigated in order to describe the various phenomena governed by anomalous reaction in dynamical systems with chaotic motion. Many authors have provided solutions of various families of fractional kinetic equations involving special functions. Here, in this paper, we aim at presenting solutions of certain general families of fractional kinetic equations using Prabhakar-type operators. The idea of present paper is motivated by Tomovski et al. [21].

• Communications for Statistical Applications and Methods
• /
• v.9 no.3
• /
• pp.629-637
• /
• 2002

Shapiro and Wilk(1972) developed a test for exponentiality with origin and scale unknown. The procedure consists of comparing the generalized least squares estimate of scale with the estimate of scale given by the sample variance. However the test based on the statistic is inconsistent Kim(2001a) proposed a modified Shapiro-Wilk's test statistic using the ratio of two asymptotically efficient estimators of scale. In this paper, we study the consistency of the proposed test.

• Journal of the Korean Statistical Society
• /
• v.30 no.1
• /
• pp.127-138
• /
• 2001

In order to combine parametric and nonparametric approaches together for survival analysis with censored observations, a new class of priors called mixtures of the beta processes is introduced. It is shown that mixtures of beta processes priors generalized the well known priors - mixtures of Dirichlet processes, and they are conjugate with right censored observations. Formulas for computing the posterior distribution are derived. Finally, a real data set is analyzed for illustrational purpose.