• Structural Engineering and Mechanics
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• v.30 no.4
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• pp.445-466
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• 2008

This paper presents a novel structural damage detection method with a new damage index based on the statistical moments of dynamic responses of a structure under a random excitation. After a brief introduction to statistical moment theory, the principle of the new method is put forward in terms of a single-degree-of-freedom (SDOF) system. The sensitivity of statistical moment to structural damage is discussed for various types of structural responses and different orders of statistical moment. The formulae for statistical moment-based damage detection are derived. The effect of measurement noise on damage detection is ascertained. The new damage index and the proposed statistical moment-based damage detection method are then extended to multi-degree-of-freedom (MDOF) systems with resort to the leastsquares method. As numerical studies, the proposed method is applied to both single and multi-story shear buildings. Numerical results show that the fourth-order statistical moment of story drifts is a more sensitive indicator to structural stiffness reduction than the natural frequencies, the second order moment of story drift, and the fourth-order moments of velocity and acceleration responses of the shear building. The fourth-order statistical moment of story drifts can be used to accurately identify both location and severity of structural stiffness reduction of the shear building. Furthermore, a significant advantage of the proposed damage detection method lies in that it is insensitive to measurement noise.

• 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.

• Communications for Statistical Applications and Methods
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• v.16 no.1
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• pp.137-141
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• 2009

We study on selecting the kernel weighting function in smoothing moment conditions for dependent processes. For hypothesis testing in Generalized Method of Moments or Generalized Empirical Likelihood context, we find that smoothing moment conditions by Bartlett kernel delivers smallest size distortions based on empirical Edgeworth expansions of the long-run variance estimator.

• Journal of the Korean Statistical Society
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• v.30 no.3
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• pp.419-433
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• 2001

In this paper we introduce a method of improving efficiency of the moment estimator of Dekkers, Einmahl and de Haan(1989) for the extreme value index $\beta$. a new estimator of $\beta$ is proposed by adding the third moment ot the original moment estimator which is composed of the first two moments of the log-transformed sample data. We establish asymptotic normality of the new estimator and examine and adaptive procedure for the new estimator. The resulting adaptive estimator proves to be asymptotically better than the moment estimator particularly for $\beta$<0.

• Journal of the Korean Statistical Society
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• v.25 no.3
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• pp.393-406
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• 1996

We obtain the general moment of non-central Wishart distribu-tion, using the J-th moment of a matrix quadratic form and the 2J-th moment of the matrix normal distribution. As an example, the second moment and kurtosis of non-central Wishart distribution are also investigated.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• Journal of the Korean Statistical Society
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• v.12 no.1
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• pp.18-23
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• 1983

Dwivedi, Srivastava and Hall(1980) derived the first and second moments of generalized ridge estimators. In this paper we consider the $m^{th}$ moment of a generalized ridge estimator and tabulate tis skewness measure.

• Korean Journal of Applied Biomechanics
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• v.16 no.4
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• pp.31-38
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• 2006

The purpose of this study was to investigate the effect of changing the steps height on the joint moment of lower extremity in stair-descent activity of elderly persons. Data were collected by 3-D cinematography and force platform. 9 male elderly subjects in the 60s and 70s participated in this study. All subjects performed a stair-descent in four different heights of stairs (10, 14, 18, 22cm) having 5 step staircase. The results were as follows. 1. For the step height of 22cm the maximum. plantarflexion moment was the smallest and the largest for the step height of 14cm. 2. There was not a statistical difference shown for the extension moment of the knee joint for the different height of steps. 3. There was not a statistical difference shown for the flexion moment of the hip joint for the varying height of steps but on average for the 18cm step this increased rapidly. 4. The smallest maximum. value for inversion moment was revealed for the step height of 10cm and this increased significantly for the step height of 22cm. 5. The smallest maximum. value for abduction moment of the hip joint was revealed for the step height of 10cm and this increased significantly for the step height of 22cm. 6. There was no significant difference shown for the maximum. abduction moment for the hip joint. The main conclusion is that there is a huge difference in the moment of the lower extremities for the elderly while walking down a stairs with a step height above 18 cm and that this moment increased or decreased rapidly under a condition of step height being 22cm. With the results from this research and related research of elderly walking upstairs it can be shown that the step height has a large role in the safety for the elderly.

• Nuclear Engineering and Technology
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• v.31 no.3
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• pp.257-266
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• 1999

A simplified statistical methodology is developed in order to both reduce over-conservatism of deterministic methodologies employed for PWR fuel rod internal pressure (RIP) calculation and simplify the complicated calculation procedure of the widely used statistical methodology which employs the response surface method and Monte Carlo simulation. The simplified statistical methodology employs the system moment method with a deterministic approach in determining the maximum variance of RIP The maximum RIP variance is determined with the square sum of each maximum value of a mean RIP value times a RIP sensitivity factor for all input variables considered. This approach makes this simplified statistical methodology much more efficient in the routine reload core design analysis since it eliminates the numerous calculations required for the power history-dependent RIP variance determination. This simplified statistical methodology is shown to be more conservative in generating RIP distribution than the widely used statistical methodology. Comparison of the significances of each input variable to RIP indicates that fission gas release model is the most significant input variable.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.323-334
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• 2003

We review the developmental history of the moment matrix of matrix quadratic form. This paper also investigates, the moment matrix of (non-central) Wishart distribution, which is multi-version of X$^2$ distribution.