On Detecting Multiple Outliers in Gamma Samples

황은영,조영석,김동희 한국자료분석학회 2017 Journal of the Korean Data Analysis Society Vol.19 No.5

In this paper, we suggest the test statistic for detecting multiple outliers in gamma distribution and derive its probability density function using characteristic function. Since the probability density function of the proposed function is very complicative, from simulation study, we present the critical values of the proposed test statistics to detect outliers easily. We also compare the powers of the proposed test statistic with other comparative statistics, Dixon (1950)’s statistic, Nooghabi et al. (2010)‘s statistic, Kumar, Lalitha (2012)’s statistic, Kim, Kim (2015)’s statistic. Throughout the simulation studies, we show that our proposed test statistic has good powers among other statistics. In particular we can inspect that the powers of our proposed test statistics are relatively good when the number of outliers, k, is greater than or equal to 2. As we know, an exponential distribution is a special case of a gamma distribution, therefore the results in this paper are applicable to an exponential distribution.

몽골 농업통계의 소개 및 발전을 위한 시사점 탐구: 한국의 농업통계 발전 경험을 참고하여

바야르마,박진우 통계청 2015 통계연구 Vol.20 No.3

As basic information for present or past state of a nation, national statistics play important roles to present national vision, to make public policies. Furthermore, they serve essential information for private sectors to make effective strategies, or to make critical decisions. Since agriculture is an important industry in Mongolia, which accounts for 21.3% of the GDP and 35% of the workforce. Democracy and the market economy system have been adopted since 1990 in Mongolia. As a result, Mongolia adopted a centralized statistical system in whice the National Statistical Office of Morngolia (MNSO) as the core. MNSO have been trying to comply with international statistical conventions and principles. Now most of the Mongolian agricultural statistics are made through censuses by the administrative organization. In 1960 South Korea was also similar circumstances. However, South Korea gradually switched to sampling surveys to increase the accuracy and efficiency of various national aricultural statistics. The purpose of this paper is to compare the agricultural statistics and statistical systems of Korea and Mongolia, and to suggest some ideas for the development of Mongolia agricultural statistics. 통계는 국가의 현 재 상황과 발전과정을 객관적으로 보여주는 기 본 정보로서 국가비전의 제 시 , 정책의 수립에 있어서 필수적인 지표일 뿐 아니라 동시에 기 업 및 개인의 전략수립과 의사결정을 위한 기초 정보로서의 기능을 담당하고 있다. 몽골에서 농업은 GDP의 21.3%, 전체 노동력의35% 를 차지할 정도로 중요한 비중을 차지하고 있으므로 농업통계의 중요성 또 한 지대하다. 몽골 은 1990년부터 다양한 형태의 재 산 소유권을 허용하는 민주주의 및 시장경제 체제로 전환하였 고 이 에 따 라 통계제도도 몽 골 통계청을 중심으로 하 는 집중형을 채택하였으며, 통계자료 수집 방법에 있어서도 국제적인 관례와 원칙을 도입하려 다양한 노력을 기울이고 있 다 . 현 재 몽골의 농업통계는 대부분 행정조직을 활용한 센서스에 의 해 작성되고 있 다 . 1960년 대 한국의 농업통계는 몽골과 비슷하게 주로 행정조직을 활용한 센서스를 통해 작성된 바 있었으나 점진적으로표본조사로 전환함으로 정확성과 효율성을 높 인 경험이 있 다 . 본 연구의 목적은 몽골과 한국의농업통계와 통계작성을 위 한 제도를 비교하고, 몽 골 농업통계 발전을 위 한 대책을 제시하는데있 다 .

Power Comparison in a Balanced Factorial Design with a Nested Factor

최영훈 한국데이터정보과학회 2008 한국데이터정보과학회지 Vol.19 No.4

In a balanced factorial design with a nested factor where crossed factors as well as a nested factor exist simultaneously, powers of the rank transformed FR statistic for testing the main, nested and interaction effects are superior to those of the parametric F statistic. In heavy tailed distributions such as exponential and double exponential distributions, powers of the FR statistic show much higher level than those of the F statistic. Further powers of the F and FR statistic for testing the main effect show the highest level in an absolute size as compared with powers of the F and FR statistic for testing the nested and interaction effects. However powers of the FR statistic for testing the nested and interaction effects rather than the main effect are greater in a relative size than powers of F statistic for the all population distributions.

Power Comparison in a Balanced Factorial Design with a Nested Factor

Choi, Young-Hun 한국데이터정보과학회 2008 한국데이터정보과학회지 Vol.19 No.4

In a balanced factorial design with a nested factor where crossed factors as well as a nested factor exist simultaneously, powers of the rank transformed FR statistic for testing the main, nested and interaction effects are superior to those of the parametric F statistic. In heavy tailed distributions such as exponential and double exponential distributions, powers of the FR statistic show much higher level than those of the F statistic. Further powers of the F and FR statistic for testing the main effect show the highest level in an absolute size as compared with powers of the F and FR statistic for testing the nested and interaction effects. However powers of the FR statistic for testing the nested and interaction effects rather than the main effect are greater in a relative size than powers of F statistic for the all population distributions.

Polynomially Adjusted Normal Approximation to the Null Distribution of Ansari-Bradley Statistic

Ha, Hyung-Tae,Yang, Wan-Youn The Korean Statistical Society 2011 응용통계연구 Vol.24 No.6

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.

Developing the Quality Assessment Indicators for the National Processing Statistics of Korea

Kim, Soo-Taek,Jeong, Ki-Ho,Kim, Seol-Hee 한국통계학회 2007 Communications for statistical applications and me Vol.14 No.3

The improvement of quality is a continuous process and one of the main objectives of the Statistical Strategy launched by the Korea National Statistical Office (KNSO) is the enhancement of the quality of Korea national statistics. In this paper, we define the processing statistic, classify the Korea national processing statistics, and develop the quality indicators and check list for assessing the national processing statistics of Korea. During its development, the indicators has been discussed with the processing statistic managers of the KNSO and the checklist tested in a pilot study covering a variety of processing statistic areas.

Empirical Comparisons of Disparity Measures for Three Dimensional Log-Linear Models

박용석,홍종선,정동빈 한국데이터정보과학회 2006 한국데이터정보과학회지 Vol.17 No.2

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

3×3 분할요인모형의 검정력 비교연구

최영훈 한국데이터정보과학회 2017 한국데이터정보과학회지 Vol.28 No.1

Restriction of completely randomization within a block can be handled by a split plot factorial design splitted by several plots. 3×3 split plot factorial design with two fixed main factors and one fixed block shows that powers of the rank transformed statistic for testing whole plot factorial effect and split plot factorial effect are superior to those of the parametric statistic when existing effect size is small or the remaining effect size is relatively smaller than the testing factorial effect size. Powers of the rank transformed statistic show relatively high level for exponential and double exponential distributions, whereas powers of the parametric and rank transformed statistic maintain similar level for normal and uniform distributions. Powers of the parametric and rank transformed statistic with two fixed main factors and one random block are respectively lower than those with all fixed factors. Powers of the parametric andrank transformed statistic for testing split plot factorial effect with two fixed main factors and one random block are slightly lower than those for testing whole plot factorial effect, but powers of the rank transformed statistic show comparative advantage over those of the parametric statistic. 블럭내의 완전랜덤화 제약은 하나의 블럭이 여러 실험구로 분할되는 분할요인모형으로 해결할 수있다. 본 연구는 3x3 분할요인모형에서 두 주요인 및 하나의 블럭이 모두 고정일 경우에는, 실제로존재하는 효과크기가 작을수록 혹은 검정대상의 요인효과 크기보다 검정대상 이외의 효과들의 크기가상대적으로 작을수록 주구요인효과 및 세구요인효과 검정을 위한 순위변환 통계량의 검정력은 기존의모수적 통계량의 검정력보다 뛰어남을 알 수 있다. 또한 모집단 모형의 오차항이 지수분포 및 이중지수분포일 때 효과크기 및 효과구성유형에 상관없이 거의 모든 상황하에서 순위변환 통계량의 검정력이 모수적 통계량의 검정력보다 상대적으로 높은 우위를 보이며, 정규분포 및 균일분포하에서는 상당히 유사한 수준을 나타낸다. 한편 두 주요인은 고정이나 하나의 블럭이 랜덤일 경우에는, 두 주요인및 블럭이 모두 고정일 경우보다 모수적 통계량 및 순위변환 통계량의 검정력은 각각 낮은 수준을 보인다. 특히 주구요인효과 검정보다 세구요인효과 검정을 위한 모수적 통계량 및 순위변환 통계량의검정력이 다소 낮은 수준임을 보이지만, 순위변환 통계량의 검정력은 모수적 통계량의 검정력에 비하여 높은 상대적 검정력 우위를 나타낸다.

Bayesian Analysis for the Ratio of Variance Components

강상길 한국데이터정보과학회 2006 한국데이터정보과학회지 Vol.17 No.2

This paper is concerned with the applicability of the chi-square approximation to the six disparity statistics: the Pearson chi-square, the generalized likelihood ratio, the power divergence, the blended weight chi-square, the blended weight Hellinger distance, and the negative exponential disparity statistic. Three dimensional contingency tables of small and moderate sample sizes are generated to be fitted to all possible hierarchical log-linear models: the completely independent model, the conditionally independent model, the partial association models, and the model with one variable independent of the other two. For models with direct solutions of expected cell counts, point estimates and confidence intervals of the 90 and 95 percentage points of six statistics are explored. For model without direct solutions, the empirical significant levels and the empirical powers of six statistics to test the significance of the three factor interaction are computed and compared.

지역통계연보 개편에 대한 제언: 전라북도 지역을 중심으로

이강진,최경호,이계민,김이수,김대경 통계청 2011 통계연구 Vol.16 No.1

As local self-governing systems have roots, demands for regional statistics needed for policy making are increasing. But the policy for the regional statistic remains standstill. In particular, one of main problems in the management of regional statistics is that regional statistical year books do not play their role. This fact is important because these are a base for all regional statistics. Thus, in this paper, we investigated several problems related to the statistical year books centering around Jeonbuk province, and suggested three reformation plans for the statistical year books: complete reformation plan based on modification of statistical standard publication and statistical administration decentralization, minimum reformation plan based on use of administrative statistics and administrative records, midium reformation plan based on reorganization and new statistical area insertion. 지방자치제가 정착됨에 따라 지역정책수립에 필요한 지역통계의 수요는 증가하고 있으나, 이에 대응하는 지역통계정책은 제자리걸음을 하고 있는 실정이다. 특히, 지역통계관리에 있어 가장 중요한 문제점 중의 하나는 지역통계연보가 그 기능을 제대로 수행하지 못하고 있는 것이다. 이 점이 중요한 이유는 지역통계연보는 지역의 모든 통계에 대한 가장 근본이 되는 통계라고 할 수 있기 때문이다. 이에 본 연구에서는 전라북도 지역통계연보를 중심으로 지역통계연보의 문제점들을 지적하고, 지역통계연보의 개편방안에 대해서 살펴보았다. 그리고 통계표준화 원칙의 수정 및 통계행정의 분권을 기반으로 한 전면개편안, 보고통계와 행정자료의 활용을 기반으로 한 최소개편안 그리고 재구성 및 신규영역의 추가를 기반으로 한 중간개편안 등 3가지 개편방안을 제시하였다.