• Journal of the Korean Statistical Society
• /
• 제28권4호
• /
• pp.443-455
• /
• 1999

A simulation-based approach to estimating the probability of an arbitrary region under a multivariate normal distribution is developed. In specific, the probability is expressed as the ratio of the unrestricted and the restricted multivariate normal density functions, where the restriction is given by the region whose probability is of interest. The density function of the restricted distribution is then estimated by using a sample generated from the Gibbs sampling algorithm.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2002년도 춘계 학술발표회 논문집
• /
• pp.73-78
• /
• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• Journal of the Korean Statistical Society
• /
• 제25권1호
• /
• pp.81-94
• /
• 1996

This paper suggests a new criterion for testing the general linear hypothesis about coefficients in multivariate growth curve model. It is developed from a Bayesian point of view using the highest posterior density region methodology. Likelihood ratio test criterion(LRTC) by Khatri(1966) results as an approximate special case. It is shown that under the simple case of vague prior distribution for the multivariate normal parameters a LRTC-like criterion results; but the degrees of freedom are lower, so the suggested test criterion yields more conservative test than is warranted by the classical LRTC, a result analogous to that of Berger and Sellke(1987). Moreover, more general(non-vague) prior distributions will generate a richer class of tests than were previously available.

• 한국수자원학회:학술대회논문집
• /
• 한국수자원학회 2008년도 학술발표회 논문집
• /
• pp.694-698
• /
• 2008

In hydrology, it is a difficult task to deal with multivariate time series such as modeling streamflows of an entire complex river system. Normal distribution based model such as MARMA (Multivariate Autorgressive Moving average) has been a major approach for modeling the multivariate time series. There are some limitations for the normal based models. One of them might be the unfavorable data-transformation forcing that the data follow the normal distribution. Furthermore, the high dimension multivariate model requires the very large parameter matrix. As an alternative, one might be decomposing the multivariate data into independent components and modeling it individually. In 1985, Lins used Principal Component Analysis (PCA). The five scores, the decomposed data from the original data, were taken and were formulated individually. The one of the five scores were modeled with AR-2 while the others are modeled with AR-1 model. From the time series analysis using the scores of the five components, he noted "principal component time series might provide a relatively simple and meaningful alternative to conventional large MARMA models". This study is inspired from the researcher's quote to develop a multivariate simulation model. The multivariate simulation model is suggested here using Principal Component Analysis (PCA) and Independent Component Analysis (ICA). Three modeling step is applied for simulation. (1) PCA is used to decompose the correlated multivariate data into the uncorrelated data while ICA decomposes the data into independent components. Here, the autocorrelation structure of the decomposed data is still dominant, which is inherited from the data of the original domain. (2) Each component is resampled by block bootstrapping or K-nearest neighbor. (3) The resampled components bring back to original domain. From using the suggested approach one might expect that a) the simulated data are different with the historical data, b) no data transformation is required (in case of ICA), c) a complex system can be decomposed into independent component and modeled individually. The model with PCA and ICA are compared with the various statistics such as the basic statistics (mean, standard deviation, skewness, autocorrelation), and reservoir-related statistics, kernel density estimate.

• Journal of the Korean Data and Information Science Society
• /
• 제22권1호
• /
• pp.107-113
• /
• 2011

We present methods for studying the log-density ratio, which allow us to select which predictors are needed, and how they should be included in the logistic regression model. Under multivariate normal distributional assumptions, we investigate the form of the log-density ratio as a function of many predictors. The linear, quadratic and crossproduct terms are required in general. If two covariance matrices are equal, then the crossproduct and quadratic terms are not needed. If the variables are uncorrelated, we do not need the crossproduct terms, but we still need the linear and quadratic terms.

• 응용통계연구
• /
• 제24권2호
• /
• pp.425-433
• /
• 2011

Reject inference in credit scoring is a statistical approach to adjust for nonrandom sample bias due to rejected applicants. Function estimation approaches are based on the assumption that rejected applicants are not necessary to be included in the estimation, when the missing data mechanism is missing at random. On the other hand, the density estimation approach by using mixture models indicates that reject inference should include rejected applicants in the model. When mixture models are chosen for reject inference, it is often assumed that data follow a normal distribution. If data include missing values, an application of the normal mixture model to fully observed cases may cause another sample bias due to missing values. We extend reject inference by a multivariate normal mixture model to handle incomplete characteristic variables. A simulation study shows that inclusion of incomplete characteristic variables outperforms the function estimation approaches.

• 한국항공우주학회지
• /
• 제49권6호
• /
• pp.521-528
• /
• 2021

위협평가가 끝난 공중항적에 대해 적절한 대응무기를 할당하기 위해서는 교전예상지점을 고려하여 교전적합성을 평가하는 것이 필요하다. 논문에서는 공중항적이 교전공간을 통과할 때 공중항적의 상대거리, 접근방위각 및 고도 등 다변량 속성정보를 가지고 베이지안 정리를 적용하여 교전공간내 위치에 따른 격추확률을 계산하는 방법을 제시하였다. 계산결과 교전공간내에서의 각 지점별 격추확률값의 분포형태는 최적의 예상요격지점을 기준으로 다변량 정규분포를 따르고 있음을 확인하였고, 계산된 격추확률값은 교전공간을 통과하는 공중항적의 교전가능성 평가에 적용가능할 것으로 기대된다.

• 품질경영학회지
• /
• 제24권4호
• /
• pp.168-189
• /
• 1996

In order for the corporation to get a good image from the customers it should consider several variables, but especially important are corproate ethics and customer satisfaction through quality improvement. Standard multivariate data analysis can be applied to find out the importance of customer satisfaction and corporate ethics as influence factors in the corporate competitive strategy. When applying this Methodology, multivariate normal distributions density function and the identical covariance between groups assumptions have to be satisfied. By using the evaluation result from a small number of specialists in an attempt to decide on the strategical factors that will create a better company image than its competitor, if it chooses to use statistical discriminant analysis method, it would be difficult to satisfy the two assumptions mentioned above. This thesis introduces discriminant analysis method that uses LP/GP effectively which is applicable to this particular situation.

• International Journal of Reliability and Applications
• /
• 제4권3호
• /
• pp.97-111
• /
• 2003

By applying Theorem 2.6.4 (Fang and Zhang, 1990, p.66) the dispersion matrix of a multivariate power exponential (MPE) distribution is derived. It is shown that the MPE and the gamma distributions are related and thus the MPE and chi-square distributions are related. By extending Fang and Xu's Theorem (1987) from the normal distribution to the Univariate Power Exponential (UPE) distribution an explicit expression is derived for calculating the probability of an UPE random variable over an interval. A representation of the characteristic function (c.f.) for an UPE distribution is given. Based on the MPE distribution the probability density functions of the generalized non-central chi-square, the generalized non-central t, and the generalized non-central F distributions are derived.

• Communications for Statistical Applications and Methods
• /
• 제6권1호
• /
• pp.237-249
• /
• 1999

It has been issued that the irreconcilability of the classical test for a point null and standard Bayesian formulation for testing such a point null. The infimum of the posterior probability of the null hypothesis is used as measure of evidence against the null hypothesis in Bayesian approach; here the infimum is over the family of priors on the alternative hypotheses which includes all density that are a priori reasonable. For iid observations from a multivariate normal distribution in $\textit{p}$ dimensions with an unknown mean and a covariance matrix propotional to the Identity we consider the difference and the Wolfowitz distance of the distributions of the P-value and the lower bound of the posterior probability over the family of all normal priors. The Wolfowitz distance is interpreted as the average difference of the quantiles of the two distrbutions.