• Communications for Statistical Applications and Methods
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• v.28 no.6
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• pp.673-679
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• 2021

The moment calculation in a truncated multivariate normal distribution is a long-standing problem in statistical computation. Recently, Kan and Robotti (2017) developed an algorithm able to calculate all orders of moment under different types of truncation. This result was implemented in an R package MomTrunc by Galarza et al. (2021); however, it is difficult to use the package in practical statistical problems because the computational burden increases exponentially as the order of the moment or the dimension of the random vector increases. Meanwhile, Lee (2021) presented an efficient numerical method in both accuracy and computational burden using Gauss-Hermit quadrature. This article introduces trunmnt implementation of Lee's work as an R package. The Package is believed to be useful for moment calculations in most practical statistical problems.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.1137-1141
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• 2004

본 연구에서는 Probability Weighted Moments의 새로운 선형조합기법인 LQ-moments를 이용하여 GEV 분포의 매개변수를 추정하고 L, LH, LQ-moments를 사용하여 뉴욕주의 Donnattsburg에 위치한 Independence River의 홍수량을 빈도 해석하였다. LH, LQ-moments가 제시된 근본적인 이유는 L-moments가 극치값에 내해 지나치게 민감한 단점을 보완하기 위해서인데, 이번 연구의 결과에 의하면 오히려 LH, LQ-moments가 극치값에 대해 민감하게 반응하여 부정확한 결과가 도출되었다. 그러므로 항상 LH, LQ-moments가 L-moments의 대안이 될 수 있는 것은 아님을 알게 되었다. 그리고 수학적 유도에서 L, LH, LQ-moments는 좀더 쉽고 간편한 메개변수 추정을 위해 Probability Weighted Moments의 선형조합을 통해 고안되었다는 공통점을 가지고 있지만, 이 점을 제외한 나머지 부분의 수식 유도에서는 서로 많은 차이가 있어서 지역적인 특성과 확률분포형의 특성을 고려하여 L, LH, LQ-moments 중에서 선별 사용해야 할 것이다.

• Journal of the Korean Data and Information Science Society
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• v.10 no.1
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• pp.19-27
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• 1999

An orientation-shift model for unit random vectors in $R^3$ is defined. The Euler angles are introduced to parametrize orientation-shifts and their moment estimators are found. Through the analytic perturbation method, the asymptotic distributions of the estimators are obtained.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.97-108
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• 2020

This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.40 no.12
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• pp.997-1003
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• 2016

This paper presents an application of adaptive algorithms for yaw moment distribution with electronic stability control (ESC) and active rear steering (ARS) in integrated chassis control (ICC). Integrated chassis control consists of upper- and lower-level controllers. In the upper-level controller, the control yaw moment is computed with sliding mode control required to stabilize a vehicle. In the lower-level controller, adaptive algorithms are applied to determine the required brake pressure of ESC and the necessary steering angle of ARS, in order to generate the control yaw moment. Simulation is performed using the vehicle simulation package CarSim to validate the proposed method.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.697-700
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• 2006

저수시 하천유량(Low Streamflow)의 추정은 하천의 수질관리, 용수공급계획, 댐 방류계획등의 수자원관리에 있어서 매우 중요한 부분이다. 이러한 중요성에 따라 Vogel과 Kroll (1989)은 저수시 하천유량을 추정하기 위한 여러 가지 확률분포함수를 제안하였다. 가장 흔히 제안되어지는 이변수 확률분포(Two-Parameter Distribution)로는 Lognormal 분포와 Weibull 분포가 있으며 이와 더불어 Three-Parameter Lognormal, Three-Parameter Weibull, Log Person Type Ⅲ 분포도 널리 사용되어진다. 그러나 이러한 여러 가지 확률 분포함수 중에서 가장 적절한 확률분포의 선택은 저수시 하천유량의 물리적인 측면과는 상관없이 주로 적합도(Gooness of Fit)에 기인된 통계치에 의해서만 결정되기도 하는데 이러한 경우 잘못된 가정을 받아들이는 확률이 높아짐에 따라 추정결과의 신뢰성(Reliability)을 감소시킬 수 있다. 이러한 문제점을 극복하기 위해서 Onoz와 Bayazit (2001)는 Recession Curve를 지수함수로 가정하고 최대 갈수 기간의 길이(Maximum Dry Period Length)의 확률에 대한 이론적인 결과치들을 사용하여 Weibull 분포의 특정한 경우에 해당되어지는 Power 분포를 유도하였으며 유도된 Power 분포의 매개변수를 추정하기 위하여 L-Moment 방법을 사용하였다. 또한 Onoz와 Bayazit (2001) 작은 유출량에서 확률분포와 잘 맞지 않는 경우 작은 유출량값에 작은 가중치를 부여하여 확률분포에 대한 영향을 줄이는 방법인 LL-Moment 방법을 제안하였다. 본 연구에서는 낙동강 유역의 1번부터 5번 소유역에 대해 SSARR 모형을 이용하여 모의한 유출량을 이용하여 Weibull 분포, L-Moment방법에 의해 추정된 매개변수를 사용한 Power 분포, LL-Moment 방법에 의해 추정된 매개변수를 사용한 Power 분포를 적용하였으며 이들 분포의 적합도를 PPCC Test를 사용하여 평가해봄으로써 낙동강 유역에서의 저수시의 유출량 추정에 대한 Power 분포의 적용성을 판단해 보았다.

• International Journal of Reliability and Applications
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• v.16 no.2
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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.

• Proceedings of the Korea Concrete Institute Conference
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• 1991.04a
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• pp.81-85
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• 1991

The object of this study is to propose the bending moment-curvature relationships based on the bond properties between concrete and steel for noncraking zone, and evaluate the flexural displacement of reinforced concrete members. The bond-slip relationship and the strain hardening effect of steel were taken into account in order to evaluate the spacing of the cracks and the curvature distribution. Calculated curvature distribution along the longitudinal axis was transformed into equivalent curvature distribution. The flexural displacement was calculated by means of double intergral of the equivalent curvature. Calculated values are in good agreement with the experimental data.

• Communications for Statistical Applications and Methods
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• v.16 no.3
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• pp.541-547
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• 2009

We consider distribution, reliability and moment of ratio in two independent beta random variables X and Y, and reliability and $K^{th}$ moment of ratio are represented by a mathematical generalized hypergeometric function. We introduce an approximate maximum likelihood estimate(AML) of reliability and right-tail probability in the beta distribution.

• Communications for Statistical Applications and Methods
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• v.18 no.6
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• pp.817-835
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• 2011

The moment(MM) and least squares(LS) estimations of the parameters are derived for the Pareto distribution in the presence of outliers. Further, we have derived a mixture method(MIX) of estimations with MM and LS that shows that the MIX is more efficient. In the final section we have given an example of actual data from a medical insurance company.