• Journal of the Korean Statistical Society
• /
• 제26권4호
• /
• pp.493-505
• /
• 1997

The analysis of binary data appears to many areas such as statistics, biometrics and econometrics. In many cases, data are often collected in which some observations are incomplete. Assume that the missing covariates are missing at random and the responses are completely observed. A method to Bayesian analysis of the binary regression model with incomplete data is presented. In particular, the desired marginal posterior moments of regression parameter are obtained using Meterpolis algorithm (Metropolis et al. 1953) within Gibbs sampler (Gelfand and Smith, 1990). Also, we compare logit model with probit model using Bayes factor which is approximated by importance sampling method. One example is presented.

• Communications for Statistical Applications and Methods
• /
• 제19권2호
• /
• pp.267-276
• /
• 2012

Bagai et al. (1989) proposed a distribution-free test for stochastic ordering in the competing risk model, and recently Murakami (2009) utilized a standard saddlepoint approximation to provide tail probabilities for the Bagai statistic under finite sample sizes. In the present paper, we consider the Gaussian-polynomial approximation proposed in Ha and Provost (2007) and compare it to the saddlepoint approximation in terms of approximating the percentiles of the Bagai statistic. We make numerical comparisons of these approximations for moderate sample sizes as was done in Murakami (2009). From the numerical results, it was observed that the Gaussianpolynomial approximation provides comparable or greater accuracy in the tail probabilities than the saddlepoint approximation. Unlike saddlepoint approximation, the Gaussian-polynomial approximation provides a simple explicit representation of the approximated density function. We also discuss the details of computations.

• Communications for Statistical Applications and Methods
• /
• 제20권6호
• /
• pp.475-480
• /
• 2013

The surplus process in a risk model is stochastically analyzed. We obtain the characteristic function of the level of the surplus at a finite time, by establishing and solving an integro-differential equation for the distribution function of the surplus. The characteristic function of the stationary distribution of the surplus is also obtained by assuming that an investment of the surplus is made to other business when the surplus reaches a sufficient level. As a consequence, we obtain the first and second moments of the surplus both at a finite time and in an infinite horizon (in the long-run).

• 한국기계연구소 소보
• /
• 통권19호
• /
• pp.61-68
• /
• 1989

As the system monitoring technology become required in order to improve the system performance and the productivity, we’ve studied to the detection for the tool wear and the tool breakage using AE sensors that is able to detection of generated high frequency stress pulse at cutting. The detection system is consist of a sensing part, a amplifier part, a signal processing part, and a analysis & output part. The moment (a rms and a kurtosis) of statistical method is used for analysis of AE singnal. The experiment are carried out in a CNC lathe. In this study, we achieved that the amplitude level of the AE signal and statistical moments was largely changed as the tool failure. The change rate of Kurtosis was especially large, but the change rate of the rms was small.

• 대한조선학회논문집
• /
• 제30권4호
• /
• pp.39-45
• /
• 1993

불규칙 해상에서의 선체의 횡동요운동을 해석하기 위하여 등가선형화방법을 사용 하였다. 일자 유도 선형 횡동요운동 모델에다가 2차의 비선형 감쇠항과 3차 및 5차의 비선형 복원 모멘트를 추가 하였으며 불규칙 기진 모멘트는 가우스 백색잡음으로 가정 하였다. 등가선형화 방법을 사용하여 예측한 응답의 통계적 특성을Simulation 결과와 비교 하였다.

• Communications for Statistical Applications and Methods
• /
• 제28권5호
• /
• pp.463-475
• /
• 2021

Desgagné and de Micheaux (2018) proposed an alternative univariate normality test to the Jarque-Bera test. The proposed statistic is based on the sample second power skewness and kurtosis while the Jarque-Bera statistic uses sample Pearson's skewness and kurtosis that are the third and fourth standardized sample moments, respectively. In this paper, we generalize their statistic to a multivariate version based on orthogonalization or an empirical standardization of data. The proposed multivariate statistic follows chi-squared distribution approximately. A simulation study shows that the proposed statistic has good control of type I error even for a very small sample size when critical values from the approximate distribution are used. It has comparable power to the multivariate version of the Jarque-Bera test with exactly the same idea of the orthogonalization. It also shows much better power for some mixed normal alternatives.

• Communications for Statistical Applications and Methods
• /
• 제29권3호
• /
• pp.333-351
• /
• 2022

The skew-t distribution is an attractive family of asymmetrical heavy-tailed densities that includes the normal, skew-normal and Student's-t distributions as special cases. In this work, we propose an EM-type algorithm for computing the maximum likelihood estimates for skew-t linear regression models with censored response. In contrast with previous proposals, this algorithm uses analytical expressions at the E-step, as opposed to Monte Carlo simulations. These expressions rely on formulas for the mean and variance of a truncated skew-t distribution, and can be computed using the R library MomTrunc. The standard errors, the prediction of unobserved values of the response and the log-likelihood function are obtained as a by-product. The proposed methodology is illustrated through the analyses of simulated and a real data application on Letter-Name Fluency test in Peruvian students.

• Communications for Statistical Applications and Methods
• /
• 제30권4호
• /
• pp.423-435
• /
• 2023

The Jarque and Bera (1980) statistic is one of the well known statistics to test univariate normality. It is based on the sample skewness and kurtosis which are the sample standardized third and fourth moments. Desgagné and de Micheaux (2018) proposed an alternative form of the Jarque-Bera statistic based on the sample second power skewness and kurtosis. In this paper, we generalize the statistic to a multivariate version by considering some data driven directions. They are directions given by the normalized standardized scaled residuals. The statistic is a modified multivariate version of Kim (2021), where the statistic is generalized using an empirical standardization of the scaled residuals of data. A simulation study reveals that the proposed statistic shows better power when the dimension of data is big.

• Journal of applied mathematics & informatics
• /
• 제41권6호
• /
• pp.1275-1301
• /
• 2023

This paper introduced the Weibull Marshall-Olkin Power Lomax (WMOPL) distribution. The statistical aspects of the proposed model are presented, such as the quantiles function, moments, mean residual life and mean deviations, variance, skewness, kurtosis, and reliability measures like the residual life function, and stress-strength reliability. The parameters of the new model are estimated using six different methods, and simulation research is illustrated to compare the six estimation methods. In the end, two real data sets show that the Weibull Marshall-Olkin Power Lomax distribution is flexible and suitable for modeling data.

• Communications for Statistical Applications and Methods
• /
• 제31권2호
• /
• pp.247-262
• /
• 2024

In this paper, we explore nonlinear sufficient dimension reduction (SDR) methods, with a primary focus on establishing a foundational framework that integrates various nonlinear SDR methods. We illustrate the generalized sliced inverse regression (GSIR) and the generalized sliced average variance estimation (GSAVE) which are fitted by the framework. Further, we delve into nonlinear extensions of inverse moments through the kernel trick, specifically examining the kernel sliced inverse regression (KSIR) and kernel canonical correlation analysis (KCCA), and explore their relationships within the established framework. We also briefly explain the nonlinear SDR for functional data. In addition, we present practical aspects such as algorithmic implementations. This paper concludes with remarks on the dimensionality problem of the target function class.