• Journal of the Korean Statistical Society
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• 제30권3호
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• pp.367-385
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• 2001

In this paper, we characterize the smoothest density with prescribed moments. Hong and Kim(1995) proved the existence and uniqueness of such as density. we introduce the general optimal control problem and prove some theorems on the characterization of the minimizer using the optimal control problem techniques.

• Journal of the Korean Statistical Society
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• 제32권2호
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• pp.193-202
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• 2003

We consider a double threshold AR-ARCH type process and give sufficient conditions under which the higher-order moments exist. Geometric ergodicity and strict stationarity are also studied.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.209-213
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• 2002

We study maximal second moment inequality and derive complete convergence for weighted sums of asymptotically almost negatively associated(AANA) random variables by applying this inequality. 2000 Mathematics Subject Classification : 60F05

• Communications for Statistical Applications and Methods
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• 제2권2호
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• pp.350-357
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• 1995

In this note, we obtain the central limit theorem for linearly positive quadrant dependent random fields satisfying some assumptions on the covariances and the moment condition $supE\mid X_i\mid^3\;<{\infty}$ The proofs are similar to those of a central limit theorem for associated random field of Cox and Grimmett.

• 대한기계학회논문집A
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• 제32권1호
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• pp.29-34
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• 2008

The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliability-based design optimization are examples of the most famous methodologies. In their formulation, the mean and standard deviation of a performance function and constraints expressed by probability conditions are involved. Therefore, it is essential to effectively and accurately calculate them and, in addition, the sensitivity results are required to obtain when the nonlinear programming is utilized during optimization process. We aim to obtain the new and efficient sensitivity formulation, which is based on integral form, on statistical moments such as the mean and standard deviation, and probability constraints. It does not require the additional functional calculation when statistical moments and failure or satisfaction probabilities are already obtained at a design point. Moreover, some numerical examples have been calculated and compared with the exact solution or the results of Monte Carlo Simulation method. The results seem to be very satisfactory.

• Structural Engineering and Mechanics
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• 제38권6호
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• pp.715-732
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• 2011

A novel structural damage detection method with a new damage index has been recently proposed by the authors based on the statistical moments of dynamic responses of shear building structures subject to white noise ground motion. The statistical moment-based damage detection (SMBDD) method is theoretically extended in this paper with general application. The generalized SMBDD method is more versatile and can identify damage locations and damage severities of many types of building structures under various external excitations. In particular, the incomplete measurements can be considered by the proposed method without mode shape expansion or model reduction. Various damage scenarios of two general forms of building structures with incomplete measurements are investigated in consideration of different excitations. The effects of measurement noise are also investigated. The damage locations and damage severities are correctly identified even when a high noise level of 15% and incomplete measurements are considered. The effectiveness and versatility of the generalized SMBDD method are demonstrated.

• 대한기계학회논문집A
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• 제31권4호
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• pp.490-495
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• 2007

This research aims to examine accuracy and efficiency of the first four moments corresponding to mean, standard deviation, skewness, and kurtosis, which are estimated by a function approximation moment method (FAMM). In FAMM, the moments are estimated from an approximating quadratic function of a system response function. The function approximation is performed on a specially selected experimental region for accuracy, and the number of function evaluations is taken equal to that of the unknown coefficients for efficiency. For this purpose, three error-minimizing conditions are utilized and corresponding canonical experimental regions constructed accordingly. An interpolation function is then obtained using a D-optimal design and then the first four moments of it are obtained as the estimates for the system response function. In order to verify accuracy and efficiency of FAMM, several non-linear examples are considered including a polynomial of order 4, an exponential function, and a rational function. The moments calculated from various coefficients of variation show very good accuracy and efficiency in comparison with those from analytic integration or the Monte Carlo simulation and the experimental design technique proposed by Taguchi and updated by D'Errico and Zaino.

• 한국전문물리치료학회지
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• 제15권2호
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• pp.64-72
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• 2008

The purpose of this study was to determine the differences in joint moment in the intact limb of uni-transfemoral amputees and to identify the implications of knee osteoarthritis. As an experimental method, three-dimensional gait analysis was performed on 10 uni-transfemoral amputees and 10 healthy males. Kinematics and kinetics at the hip, knee, and ankle joint were calculated. As a statistical method, independent t-tests were conducted to perform a comparison between the transfemoral amputee group and the control group. The results showed that the external knee adduction moment increased in the transfemoral amputee group (.22 Nm/kg) compared with that of the control group (.13 Nm/kg) at terminal stance (p=.008). External knee flexion moment also increased in the transfemoral amputee group (.24 Nm/kg) but this difference was not statistically significant. External hip flexion moment increased in the transfemoral amputee group (1.35 Nm/kg) compared with that of the control group (.45 Nm/kg) at initial stance, and external hip extension moment decreased in the transfemoral amputee group (-.26 Nm/kg) compared with that of the control group (-.76 Nm/kg) at terminal stance. Although external ankle plantarflexion moment of the transfemoral amputee group increased, it was not found to be statistically significant. The results suggest that the intact limb joint moment of the uni-transfemoral amputees during walking can be different from that of healthy subjects. In conclusion, it was found that there is a link between the increase of external knee adduction moment and the prevalence of knee osteoarthritis in uni-transfemoral amputees. This result is expected to provide some objective data for rehabilitation programs related to knee osteoarthritis in transfemoral amputees.

• Journal of the Korean Statistical Society
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• 제21권2호
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• pp.187-200
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• 1992

Samples are often found to be too heterogeneous to be explained by a one-parameter family of models in the sense that the implicit mean-variance relationship in such a family is violated by the data. This phenomenon is often called over-dispersion. The most frequently used method in dealing with over-dispersion is to mix a one-parameter family creating a two parameter marginal mixture family for the data. In this paper, we investigate performance of estimators such as maximum likelihood estimator, method of moment estimator, and maximum quasi-likelihood estimator in negative binomial and beta-binomial distribution. Simulations are done for various mean parameter and dispersion parameter in both distributions, and we conclude that the moment estimators are very superior in the sense of bias and asymptotic relative efficiency.

• International Journal of Reliability and Applications
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• 제16권2호
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• pp.81-98
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• 2015

The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the $r^{th}$ moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.