• 한국국방경영분석학회지
• /
• 제9권2호
• /
• pp.39-43
• /
• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• 통합자연과학논문집
• /
• 제7권3호
• /
• pp.208-213
• /
• 2014

National-wide and/or large scale sample surveys generally use complex sample design. Traditional Pearson chi-square test is not appropriate for the categorical complex sample data. Rao-Scott suggested an adjustment method for Pearson chi-square test, which uses the average of eigenvalues of design matrix of cell probabilities. This study is to compare the efficiency of Rao-Scott first order adjusted test to Wald test for homogeneity between two populations using 2009 Gyeongnam regional education offices's customer satisfaction survey (2009 GREOCSS) data. The 2009 GREOCSS data were collected based on stratified three-stage cluster sampling with probability proportional to size. The empirical results show that the Rao-Scott adjusted test statistic using only the variances of cell probabilities is very close to the Wald test statistic, which uses the covariance matrix of cell probabilities, under the 2009 GREOCSS data based. However it is necessary to be cautious to use the Rao-Scott first order adjusted test statistic in the place of Wald test because its efficiency is decreasing as the relative variance of eigenvalues of the design matrix of cell probabilities is increasing, specially more when the number of degrees of freedom is small.

• Communications for Statistical Applications and Methods
• /
• 제18권6호
• /
• pp.787-798
• /
• 2011

In this paper, we develop some characterization results in terms of survival entropy of the first order statistic. In addition, we generalize the cumulative entropy recently proposed by Di Crescenzo and Logobardi (2009) to a new measure of information (called the failure entropy) and study some properties of it and its dynamic version. Furthermore, power distribution is characterized based on dynamic failure entropy.

• Journal of the Korean Statistical Society
• /
• 제26권3호
• /
• pp.365-382
• /
• 1997

In this paper we study the behaviors of the generalized Durbin-Watson (DW) statistics when the nonstationary seasonal time series regression model is misspecified. It is observed that when the series is seasonally integrated the generalized DW statistic for the seasonal period order autocorrelation converges in probability to zero while teh generalized DW statistic for the first order autocorrelation has nondegenerate asymptotic distribution. When the series is regularly and seasonally integrated the generalized DW for the first order autocorrelation still converges in probability to zero.

• Geosystem Engineering
• /
• 제21권5호
• /
• pp.262-272
• /
• 2018

The U-statistic method is one of the most important structural methods to separate the anomaly from background. It considers the location of samples and carries out the statistical analysis of the data without judging from a geochemical point of view and tries to separate subpopulations and determine anomalous areas. In the present study, 3D U-statistic method has been applied for the first time through the three-dimensional (3D) modeling of an ore deposit. In order to achieve this purpose, 3D U-statistic is applied on the data (Fe grade) resulted from the drilling network in Baghak mine, central part of the Sangan iron mines (in Khorassan Razavi Province, Iran). Afterward, results from applying 3D U-statistic method are used for 3D modeling of the iron mineralization. Results show that the anomalous values are well separated from background so that the determined samples as anomalous are not dispersed and according to their positioning, denser areas of anomalous samples could be considered as anomaly areas. And also, final results (3D model of iron mineralization) show that output model using this method is compatible with designed model for mining operation. Moreover, seen that U-statistic method in addition for separating anomaly from background, could be very efficient for the 3D modeling of different ore type.

• Communications for Statistical Applications and Methods
• /
• 제5권2호
• /
• pp.411-416
• /
• 1998

A simple nonparametric test of complete or total independence is suggested for continuous multivariate distributions. This procedure first discretizes the original variables based on their order statistics, and then tests the hypothesis of complete independence for the resulting contingency table. Under the hypothesis of independence, the chi-squared test statistic has an asymptotic chi-squared distribution. We present a simulation study to illustrate the accuracy in finite samples of the limiting distribution of the test statistic. We compare our method to another nonparametric test of complete independence via a simulation study. Finally, we apply our method to the residuals from a real data set.

• 응용통계연구
• /
• 제24권6호
• /
• pp.1161-1168
• /
• 2011

The approximation for the distribution functions of nonparametric test statistics is a significant step in statistical inference. A rank sum test for dispersions proposed by Ansari and Bradley (1960), which is widely used to distinguish the variation between two populations, has been considered as one of the most popular nonparametric statistics. In this paper, the statistical tables for the distribution of the nonparametric Ansari-Bradley statistic is produced by use of polynomially adjusted normal approximation as a semi parametric density approximation technique. Polynomial adjustment can significantly improve approximation precision from normal approximation. The normal-polynomial density approximation for Ansari-Bradley statistic under finite sample sizes is utilized to provide the statistical table for various combination of its sample sizes. In order to find the optimal degree of polynomial adjustment of the proposed technique, the sum of squared probability mass function(PMF) difference between the exact distribution and its approximant is measured. It was observed that the approximation utilizing only two more moments of Ansari-Bradley statistic (in addition to the first two moments for normal approximation provide) more accurate approximations for various combinations of parameters. For instance, four degree polynomially adjusted normal approximant is about 117 times more accurate than normal approximation with respect to the sum of the squared PMF difference.

• Management Science and Financial Engineering
• /
• 제2권1호
• /
• pp.103-122
• /
• 1996

This paper presents an easily used graphical procedure for simultaneous estimation of the index, skewness, scale, and location parameters of the stable laws. First, the index $\alpha$ and skewness $\beta$ are estimated through the joint use of a tail length statistic $\widetilde{K_t}$ and a skewness statistic $\widetilde{K_s}$, both of which are functions of order statistics. Next, the function of order statistics needed for estimation of scale $\sigma$ and location $\mu$ are determined from a nomogram indexed on the estimates of $\alpha$ and $\beta$. Some applications and examples are provided.

• Journal of the Korean Statistical Society
• /
• 제27권2호
• /
• pp.189-195
• /
• 1998

In this paper, we are concerned with the problem of testing the randomness of the coefficients in a first order autoregressive model. A consistent test based on prediction error is suggested. It is shown that under the null hypothesis, the test statistic is asymptotically normal.

• 응용통계연구
• /
• 제27권7호
• /
• pp.1163-1170
• /
• 2014

간헐적인 패널 시계열 자료의 개념과 구조를 소개하고, 간헐적인 패널 시계열 자료의 모형으로 간헐적인 패널 1차 자기회귀 모형을 고려하였다. 간헐적인 패널 1차 자기회귀 모형의 동질성 검정을 위하여 Wald 검정통계량을 제안하고, 그 극한분포를 제시하였다. 또한 동질성이 만족되는 경우 시점 별 평균을 이용하여 종합한 자료로 모형을 적합하였다. 이 모형의 동질성 검정 통계량의 극한분포가 $^x2$분포에 잘 따르는지를 알아보기 위해 모의실험을 실시하고, 실제 자료 분석으로 지역별 월별 Mumps 자료에 간헐적인 패널 1차 자기회귀 모형을 적합하여 동질성 검정을 수행한 결과 동질성을 만족하였다. 동질성이 만족된 지역별 월별 Mumps 자료를 시점 별 평균을 이용하여 종합하고 1차 자기회귀 모형으로 적합하였다.