STATISTICS PRESENT, NEAR FUTURE, AND BEYOND

Johnson, Richard A. The Korean Statistical Society 2001 Communications for statistical applications and me Vol.8 No.-

We berlin with a brief review of some important advances made in statistical theory over the last decade. The choice of topics is decidedly influenced by personal interests. Based on this review, we then propose some possible scenarios about the future of statistics.

Design of On-line Process Control with Variable Measurement Interval

Park, Changsoon The Korean Statistical Society 2000 Journal of the Korean Statistical Society Vol.29 No.3

A mixed model with a white noise process and an IMA(0,1,1) process is considered as a process model. It is assumed that the process is a white noise in the absence of a special cause and the process changes to an IMA(0,1,1) due to a special cause. One useful scheme in measuring the process level is to use the variable measurement interval (VMI) between measurement times according to the value of the previous chart statistic. The advantage of the VMI scheme is to measure the process level infrequently when in control to save the measurement cost and to measure frequently when out of control to save the off-target cost. This paper considers the VMI scheme in order to detect changes in the process model from a white noise to an IMA(0,1,1). The VMI scheme is shown to be effective compared to the standard fixed measurement interval (FMI) scheme in both statistical and economic contexts.

Statistical Bias and Inflated Variance in the Genehunter Nonparametric Linkage Test Statistic

Song, Hae-Hiang,Choi, Eun-Kyeong The Korean Statistical Society 2009 Communications for statistical applications and me Vol.16 No.2

Evidence of linkage is expressed as a decreasing trend of the squared trait difference of two siblings with increasing identical by descent scores. In contrast to successes in the application of a parametric approach of Haseman-Elston regression, notably low powers are demonstrated in the nonparametric linkage analysis methods for complex traits and diseases with sib-pairs data. We report that the Genehunter nonparametric linkage statistic is biased and furthermore the variance formula that they used is an inflated one, and this is one reason for a low performance. Thus, we propose bias-corrected nonparametric linkage statistics. Simulation studies comparing our proposed nonparametric test statistics versus the existing test statistics suggest that the bias-corrected new nonparametric test statistics are more powerful and attains efficiencies close to that of Haseman-Elston regression.

SOME GENERALIZED GAMMA DISTRIBUTION

Nadarajah Saralees,Gupta Arjun K. The Korean Statistical Society 2007 Journal of the Korean Statistical Society Vol.36 No.1

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

Kullback-Leibler Information of Consecutive Order Statistics

Kim, Ilmun,Park, Sangun The Korean Statistical Society 2015 Communications for statistical applications and me Vol.22 No.5

A calculation of the Kullback-Leibler information of consecutive order statistics is complicated because it depends on a multi-dimensional integral. Park (2014) discussed a representation of the Kullback-Leibler information of the first r order statistics in terms of the hazard function and simplified the r-fold integral to a single integral. In this paper, we first express the Kullback-Leibler information in terms of the reversed hazard function. Then we establish a generalized result of Park (2014) to an arbitrary consecutive order statistics. We derive a single integral form of the Kullback-Leibler information of an arbitrary block of order statistics; in addition, its relation to the Fisher information of order statistics is discussed with numerical examples provided.

A Bayes Reliability Estimation from Life Test in a Stress-Strength Model

Park, Sung-Sub,Kim, Jae-Joo The Korean Statistical Society 1983 Journal of the Korean Statistical Society Vol.12 No.1

A stress-strength model is formulated for s out of k system of identical components. We consider the estimation of system reliability from survival count data from a Bayesian viewpoint. We assume a quadratic loss and a Dirichlet prior distribution. It is shown that a Bayes sequential procedure can be established. The Bayes estimator is compared with the UMVUE obtained by Bhattacharyya and with an estimator based on Mann-Whitney statistic.

VUS and HUM Represented with Mann-Whitney Statistic

Hong, Chong Sun,Cho, Min Ho The Korean Statistical Society 2015 Communications for statistical applications and me Vol.22 No.3

The area under the ROC curve (AUC), the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) are defined and interpreted with probability that measures the discriminant power of classification models. AUC, VUS and HUM are expressed with the summation and integration notations for discrete and continuous random variables, respectively. AUC for discrete two random samples is represented as the nonparametric Mann-Whitney statistic. In this work, we define conditional Mann-Whitney statistics to compare more than two discrete random samples as well as propose that VUS and HUM are represented as functions of the conditional Mann-Whitney statistics. Three and four discrete random samples with some tie values are generated. Values of VUS and HUM are obtained using the proposed statistic. The values of VUS and HUM are identical with those obtained by definition; therefore, both VUS and HUM could be represented with conditional Mann-Whitney statistics proposed in this paper.

A Multiple Unit Roots Test Based on Least Squares Estimator

Shin, Key-Il The Korean Statistical Society 1999 Journal of the Korean Statistical Society Vol.28 No.1

Knowing the number of unit roots is important in the analysis of k-dimensional multivariate autoregressive process. In this paper we suggest simple multiple unit roots test statistics based on least squares estimator for the multivariate AR(1) process in which some eigenvalues are one and the rest are less than one in magnitude. The empirical distributions are tabulated for suggested test statistics. We have small Monte-Calro studies to compare the powers of the test statistics suggested by Johansen(1988) and in this paper.

Test Statistics for Volume under the ROC Surface and Hypervolume under the ROC Manifold

Hong, Chong Sun,Cho, Min Ho The Korean Statistical Society 2015 Communications for statistical applications and me Vol.22 No.4

The area under the ROC curve can be represented by both Mann-Whitney and Wilcoxon rank sum statistics. Consider an ROC surface and manifold equal to three dimensions or more. This paper finds that the volume under the ROC surface (VUS) and the hypervolume under the ROC manifold (HUM) could be derived as functions of both conditional Mann-Whitney statistics and conditional Wilcoxon rank sum statistics. The nullhypothesis equal to three distribution functions or more are identical can be tested using VUS and HUM statistics based on the asymptotic large sample theory of Wilcoxon rank sum statistics. Illustrative examples with three and four random samples show that two approaches give the same VUS and $HUM^4$. The equivalence of several distribution functions is also tested with VUS and $HUM^4$ in terms of conditional Wilcoxon rank sum statistics.

Testing Hypothesis for the Logistic Model with Estimated Parameters : Modified Tables of Cirticla Values for K-S Type Statistic

Hwang, Chung-Sun The Korean Statistical Society 1984 Journal of the Korean Statistical Society Vol.13 No.1

This paper considers one-sample and two-sample test for the logistic function by means of Kolmororov-Smirnov type statistics. The standard tables used for the Kolmogorov-Smirnov test are valid only when the function is completely specified; but they are not valid if the parameters of function are estimated from the sample. This note presents modified tables for the Kolmogorov-Sminov type staistic. These tables can be used to test the hypothesis that a sample comes from a logistic function when shape parameter $(\alpha)$ and location parameter $(\beta)$ must be estimated from the sample by the method of maximum likelihood. Monte Carlo method is employed to calculate the criticla values of the test. The tables of the critical values are provided.