• Communications for Statistical Applications and Methods
• /
• v.15 no.3
• /
• pp.429-440
• /
• 2008

In this paper, we develop the noninformative priors when the parameter of interest is the common coefficient of variation in two inverse Gaussian distributions. We want to develop the first and second order probability matching priors. But we prove that the second order probability matching prior does not exist. It turns out that the one-at-a-time and two group reference priors satisfy the first order matching criterion but Jeffreys' prior does not. The Bayesian credible intervals based on the one-at-a-time reference prior meet the frequentist target coverage probabilities much better than that of Jeffreys' prior. Some simulations are given.

• Communications for Statistical Applications and Methods
• /
• v.22 no.6
• /
• pp.531-542
• /
• 2015

In this survey, we use the normal linear model to demonstrate the use of the linear Bayes method. The superiorities of linear Bayes estimator (LBE) over the classical UMVUE and MLE are established in terms of the mean squared error matrix (MSEM) criterion. Compared with the usual Bayes estimator (obtained by the MCMC method) the proposed LBE is simple and easy to use with numerical results presented to illustrate its performance. We also examine the applications of linear Bayes method to some other distributions including two-parameter exponential family, uniform distribution and inverse Gaussian distribution, and finally make some remarks.

• Wind and Structures
• /
• v.31 no.6
• /
• pp.549-560
• /
• 2020

Methods for stochastic simulation of non-Gaussian wind pressure have increasingly addressed the efficiency and accuracy contents to offer an accurate description of the extreme value estimation of the long-span and high-rise structures. This paper presents a linear prediction and z-transform (LPZ) based Cumulative distribution function (CDF) mapping algorithm for the simulation of multivariate non-Gaussian fluctuating wind pressure. The new algorithm generates realizations of non-Gaussian with prescribed marginal probability distribution function (PDF) and prescribed spectral density function (PSD). The inverse linear prediction and z-transform function (ILPZ) is deduced. LPZ is improved and applied to non-Gaussian wind pressure simulation for the first time. The new algorithm is demonstrated to be efficient, flexible, and more accurate in comparison with the FFT-based method and Hermite polynomial model method in two examples for transverse softening and longitudinal hardening non-Gaussian wind pressures.

• Journal of the Korean Statistical Society
• /
• v.13 no.2
• /
• pp.73-80
• /
• 1984

In this paper, likelihood-ratio test has been derived for testing multisample sphericity in complex multivariate Gaussian populations. The $h^{th}$ moment of the test statistic is given and its exact distribution has been derived using inverse Mellin transform. Asymptotic distribution of the statistic is also given.

• Journal of the Korean Society for Advanced Composite Structures
• /
• v.1 no.2
• /
• pp.51-58
• /
• 2010

This work examines the identification of stiffness reduction in damaged reinforced concrete bridges under moving loads, and carries out the performance assessment after repairing using advanced composite materials. In particular, the change of stiffness in each element before and after repairing, based on the Microgenetic algorithm as an advanced inverse analysis, is described and discussed by using a modified bivariate Gaussian distribution function. The proposed method in the study is more feasible than the conventional element-based method from computation efficiency point of view. The validity of the technique is numerically verified using a set of dynamic data obtained from a simulation of the actual bridge modeled with a three-dimensional solid element. The numerical examples show that the proposed technique is a feasible and practical method which can inspect the complex distribution of deteriorated stiffness although there is a difference between actual bridge and numerical model as well as uncertain noise occurred in the measured data.

• Korean Journal of Optics and Photonics
• /
• v.8 no.2
• /
• pp.95-98
• /
• 1997

The Gaussian diffraction pattern initially assumed in the diffraction inverse problem is further sharply defined by multiplying $e^{-q{\omega}_0$\mid${\chi}$\mid$}$. The modified pupil function is obtained and the diffraction intensity distribution for the finite aperture ($-{\omega}_0~{\times}{\omega}_0$ is obtained, and then the OTF is derived analytically. It is found the OTF is equal to or less than the $(OTF)_{q=0}$, namely the modulation is not useful. It is shown that the narrowing down the initial Gaussian diffraction pattern does not give the anticipated improvement in OTF and the reason is clarified.

• Communications for Statistical Applications and Methods
• /
• v.28 no.1
• /
• pp.59-79
• /
• 2021

Value at Risk (VaR) is one of the most common risk management tools in finance. Since a portfolio of several assets, rather than one asset portfolio, is advantageous in the risk diversification for investment, VaR for a portfolio of two or more assets is often used. In such cases, multivariate distributions of asset returns are considered to calculate VaR of the corresponding portfolio. Copulas are one way of generating a multivariate distribution by identifying the dependence structure of asset returns while allowing many different marginal distributions. However, they are used mainly for bivariate distributions and are not widely used in modeling joint distributions for many variables in finance. In this study, we would like to examine the performance of various copulas for high dimensional data and several different dependence structures. This paper compares copulas such as elliptical, vine, and hierarchical copulas in computing the VaR of portfolios to find appropriate copula functions in various dependence structures among asset return distributions. In the simulation studies under various dependence structures and real data analysis, the hierarchical Clayton copula shows the best performance in the VaR calculation using four assets. For marginal distributions of single asset returns, normal inverse Gaussian distribution was used to model asset return distributions, which are generally high-peaked and heavy-tailed.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
• /
• v.2B no.4
• /
• pp.168-173
• /
• 2002

A new identification algorithm for the Preisach model is presented. The algorithm treats the identification procedure of the Preisach model as an inverse problem where the independent variables are parameters of the distribution function and the objective function is constructed using only the initial magnetization curve or only tile major loop of the hysteresis curve as well as the whole reversal curves. To parameterize the distribution function, the Bezier spline and Gaussian function are used for the coercive and interaction fields axes, respectively. The presented algorithm is applied to the ferrite permanent magnets, and the distribution functions are correctly found from the major loop of the hysteresis curve or the initial magnetization curve.

• The Journal of the Acoustical Society of Korea
• /
• v.13 no.6
• /
• pp.66-74
• /
• 1994

Simulation of sonar reverberation time series is very useful because most acoustic models are power level models and have a difficulty when performance of hardware system is evaluated under the reverberant condition. Thus, in this paper, the simulation of reverberation time series is attempted, First, normalized spectrum, whose bandwidth is varying in the frequency domain and which has zero-mean Gaussian distribution, is calculated at pre-selected receiving time. Second, reverberation levels given by underwater acoustic model are combined with normalized spectrum in the frequency domain. Finally, nonstationary sonar reverberation time series are simulated by IFT(Inverse Fourier Transform).

• The Journal of the Acoustical Society of Korea
• /
• v.15 no.4E
• /
• pp.3-8
• /
• 1996

The bubble size distribution is critical information to understand sound propagation and ambient noise in the ocean. To estimate the bubble size distribution in a bubbly water, the sound attenuation has been only in the conventional acoustic bubble sizing method without considering the sound speed variation. However, the effect of the sound speed variation in bubbly water cannot be neglected because of its compressibility variation. The sound attenuation is also affected by the sound speed variation. In this paper, a coherent acoustic bubble sizing inverse technique is introduced as a new bubble sizing technique with considering sound speed variation as well as the sound attenuation. This coherent sizing method is theoretically verified with the bubble distribution functions of single-size, Gaussian, and power-law functions. Its numerical test results with the coherent acoustic bubble sizing method show good agreement with the given bubble distributions.