• Communications for Statistical Applications and Methods
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• v.3 no.2
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• pp.283-290
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• 1996

For finite discrete distributions with prescribed moments, there is a well-known upper bound on the index of the support. In this paper, we are interested in the smoothest density with prescribed moments among the class of smooth functions. We define an index of continuous distribution through the support and derive an upper bound on the index of the smoothest density. Some examples are given, some of which achieve the upper bound.

• Journal of the Korean Statistical Society
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• v.30 no.3
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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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• v.32 no.2
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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.

• Proceedings of the Korean Statistical Society Conference
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• 2004.11a
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• pp.91-95
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• 2004

Moments of skew t random vectors and their quadratic forms are derived. It is shown that the moments of the sample autocovariance function and of the sample variogram estimator do not depend on a skewness parameter.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.349-355
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• 2007

In this paper we study some important properties of the bivariate generalized hypergeometric probability (BGHP) distribution by establishing the existence of all the moments of the distribution and by deriving recurrence relations for raw moments. It is shown that certain mixtures of BGHP distributions are again BGHP distributions and a limiting case of the distribution is considered.

• The Journal of Korea Robotics Society
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• v.16 no.2
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• pp.103-111
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• 2021

This study addresses a low-cost lidar sensor-based glass feature extraction method for an accurate map representation using statistical moments, i.e. the mean and variance. Since the low-cost lidar sensor produces range-only data without intensity and multi-echo data, there are some difficulties in detecting glass-like objects. In this study, a principle that an incidence angle of a ray emitted from the lidar with respect to a glass surface is close to zero degrees is concerned for glass detection. Besides, all sensor data are preprocessed and clustered, which is represented using statistical moments as glass feature candidates. Glass features are selected among the candidates according to several conditions based on the principle and geometric relation in the global coordinate system. The accumulated glass features are classified according to the distance, which is lastly represented on the map. Several experiments were conducted in glass environments. The results showed that the proposed method accurately extracted and represented glass windows using proper parameters. The parameters were empirically designed and carefully analyzed. In future work, we will implement and perform the conventional SLAM algorithms combined with our glass feature extraction method in glass environments.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.11
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• pp.1691-1696
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• 2010

The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliabilitybased design optimization are examples of the most famous methodologies. The statistical moments of a performance function and the constraints corresponding to probability conditions are involved in the formulation of these methodologies. Therefore, it is essential to effectively and accurately calculate them. The sensitivities of these methodologies have to be determined when nonlinear programming is utilized during the optimization process. The sensitivity of statistical moments and probability constraints is expressed in the integral form and limited to the normal random variable; we aim to expand the sensitivity formulation to nonnormal variables. Additional functional calculation will not be required when statistical moments and failure or satisfaction probabilities are already obtained at a design point. On the other hand, the accuracy of the sensitivity results could be worse than that of the moments because the target function is expressed as a product of the performance function and the explicit functions derived from probability density functions.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.31 no.4
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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.

• Communications for Statistical Applications and Methods
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• v.24 no.5
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• pp.421-441
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• 2017

In this survey, estimation methods for structural vector autoregressive models are presented in a systematic way. Both frequentist and Bayesian methods are considered. Depending on the model setup and type of restrictions, least squares estimation, instrumental variables estimation, method-of-moments estimation and generalized method-of-moments are considered. The methods are presented in a unified framework that enables a practitioner to find the most suitable estimation method for a given model setup and set of restrictions. It is emphasized that specifying the identifying restrictions such that they are linear restrictions on the structural parameters is helpful. Examples are provided to illustrate alternative model setups, types of restrictions and the most suitable corresponding estimation methods.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.19 no.6
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• pp.1004-1015
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• 1994

Modulation type classifier based on statistical moments has been successfully employed to classify PSK signals. Previously, the classifier developed utilizes the statistical moment of samples of the received signal phase, which may be difficult to extract from received signal. In this paper we propose a new moments-based classifier to classify PSK signals by using the moments of the demodulated signal for PSK. THe demodulated signal can be easily extracted from the conventional demodulation of PSK. The evaluation of the performance of the proposed classifier for PSK signals has been investigated in additive white Gaussian noise environment using the exact distribution of the demodulated signal. The performances of classifier in terms of probability of misclassification were evaluated. We found that the coherent system classifier gave 4dB improvement for BPSK and 3dB for QPSK over noncoherent system classifier, when the probability of misclassification is 10 and m equals to 4.