• The Korean Journal of Applied Statistics
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• v.24 no.2
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• pp.383-391
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• 2011

This paper presents a modified entropy-based test of fit for the inverse Gaussian distribution. The test is based on the entropy difference of the unknown data-generating distribution and the inverse Gaussian distribution. The entropy difference estimator used as the test statistic is obtained by employing Vasicek's sample entropy as an entropy estimator for the data-generating distribution and the uniformly minimum variance unbiased estimator as an entropy estimator for the inverse Gaussian distribution. The critical values of the test statistic empirically determined are provided in a tabular form. Monte Carlo simulations are performed to compare the proposed test with the previous entropy-based test in terms of power.

• Journal of Korean Society of Coastal and Ocean Engineers
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• v.32 no.1
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• pp.26-38
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• 2020

A statistical test was carried out on the IID (Independently and Identically Distributed) assumption of the AM (Annual Maxima) data used to estimate the design wave height. The test was divided into independence (randomness) test and homogeneity test, and each test was conducted on AM data of 210 and 310 stations in coastal and inner coastal grids in typhoon and non-typhoon (monsoon) conditions. As a result of the independence test, the rejection ratios of the test are in the range of 1.8~5.3% and 1.4~6.0% for the non-typhoon and typhoon data sets, respectively. On the other hand, in the distribution difference test of typhoon data and nontyphoon data, the same distribution hypothesis was found to be rejected in the range of 47~79% according to the test method for both coastal grid and inner coastal grid. Therefore, in estimating design wave height by extreme value analysis, the estimation process by dividing the typhoon and non-typhoon data is appropriate.

• Proceedings of the Korea Water Resources Association Conference
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• 2017.05a
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• pp.412-412
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• 2017

강우빈도해석을 위해서는 확률분포선정이 우선적으로 이루어져야 한다. 우리나라에서는 사용상의 편리상, 기존 해석결과와의 연속성 등을 이유로 Gumbel 확률분포가 가장 일반적으로 활용되고 있다. 그러나, 분포형 선정에 따른 확률강수량의 차이가 크게 발생한다는 점에서 단순히 해석상의 편리성을 기준으로 분포형 선정이 이루어지는 것은 바람직하지 않다. 특히, 우리나라에서 강우빈도해석 시 분포형 선정은 형식적인 수준에 그치고 있으며, 주로 KS검정, 검정 등 적합도 검정을 통해 고려된 분포형의 통계적 유의성만을 평가하고 있다. 그러나, 최적 분포형 선정이라는 관점에서 이러한 유의성 검정보다는 정량적인 지표를 기준으로 확률분포형 선정이 이루어지는 것이 적합할 것으로 판단된다. 즉, 자료의 설명력이 가장 우수한 분포를 정량적 지표를 기준으로 추정하는 것이 수문통계학적으로 적합성을 갖는다. 이러한 점에서 본 연구에서는 우도함수, BIC 및 AIC를 기준으로 우리나라 주요 강수지점에서 대해서 최적 분포형을 선정하고, 기존 Gumbel 분포를 기준으로 산정된 확률강수량과의 양적차이를 평가해보고자 한다.

• Communications for Statistical Applications and Methods
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• v.4 no.2
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• pp.533-540
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• 1997

일반화 감마분포(generalized gamma distribution)에서 지표모수(index parameter)에 대한 추론은 생존시간(lifetime)과 관련한 모형의 선택문제에서 매우 중요하다. 이에 대한 정확한(exact) 추론법은 알려져 있지 않다. 본 연구에서는 이에 대한 점근적(asymptotic) 검정법으로 소표본에서도 우도비 검정에 비해 효율이 뛰어난 Bartlett 검정을 제안하고, 이의 요율적 수행을 위한 대체 모형으로 부터의 누율계산(cumulant computation) 법을 제시하였다. 또한 실제자료에 대해 본 논문에서 제시한 누율계산과정을 이용하여 Bartlett 검정을 실시한 결과 기존의 우도비 검정과는 상당히 큰 차이가 남을 확인하였다. 따라서 모형의 선택 등의 문제에서 제안된 방법은 소표본의 경우에 더욱 효율적이라 할 수 있다.

• Proceedings of the Korea Water Resources Association Conference
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• 2006.05a
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• pp.169-173
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• 2006

일반적으로 확률수문량을 산정하기 위해서는 수문자료에 대해 빈도해석을 실시한 후 확률수문량을 산정하게 된다. 재현기간이 커질수록 확률분포형에 따라 확률수문량의 값은 많은 차이를 나타내므로 적정 확률분포형의 선정은 매우 중요하다고 할 수 있다. 적정 확률분포형의 선정은 객관적인 기준에 의해 이루어져야 하나, 적정 확률분포형의 선정에 있어 명확한 기준이 마련되어 있지 않아 실무에서 확률수문량을 산정할 때 많은 어려움을 겪고 있는 실정이다. 따라서 본 연구에서는 적정 확률분포형의 선정기준으로 제시되어 있는 검정통계량을 이용한 방법의 적용성을 비교 검토하고자 한다. 이를 위해 우리나라에서 널리 사용되고 있는 Gumbel, GEV 분포형과 Weibull, Generalized logistic 분포형을 선택하고 각각의 분포형에 대해 자료의 크기별 모의를 통해 자료를 발생시킨 후 빈도해석을 수행하고, 적합도 검정 단계에서 산출되는 검정통계량을 비교하여 적정 확률분포형을 선정하여 적용성을 검토하고자 한다. 결과적으로 자료 발생에 이용된 분포형과는 관계없이 자료수가 작을수록 2변수 gamma, 자료수가 많을수록 5변수 Wakeby가 제일 많이 선정되는 것으로 나타났으며, Gumbel, GEV, generalized logistic 분포형의 경우는 대체로 자료의 수가 많아질수록 선정되는 빈도가 많은 것으로 나타났다.

• Journal of the Korean Data and Information Science Society
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• v.11 no.2
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• pp.269-277
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• 2000

We propose the Bayesian testing for the equality of two log-normal population means. Specifically we use the intrinsic Bayes factors suggested by Berger and Perichi (1996, 1998) based on the noninformative priors for the parameters. In order to investigate the usefulness of the proposed Bayesian testing procedures, we compare it with classical tests via both real data analysis and simulation.

• The Korean Journal of Applied Statistics
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• v.30 no.4
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• pp.579-590
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• 2017

The multivariate empirical distribution function could be defined when its distribution function can be estimated. It is known that bivariate empirical distribution functions could be visualized by using Step plot and Quantile plot. In this paper, the multivariate empirical distribution plot is proposed to represent the multivariate empirical distribution function on the unit square. Based on many kinds of empirical distribution plots corresponding to various multivariate normal distributions and other specific distributions, it is found that the empirical distribution plot also depends sensitively on its distribution function and correlation coefficients. Hence, we could suggest five goodness-of-fit test statistics. These critical values are obtained by Monte Carlo simulation. We explore that these critical values are not much different from those in text books. Therefore, we may conclude that the proposed test statistics in this work would be used with known critical values with ease.

• The KIPS Transactions:PartB
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• v.9B no.3
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• pp.271-276
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• 2002

The test statistic in ANOVA tests has a single or doubly noncentral F distribution and the noncentral F distribution is applied to the calculation of the power functions of tests of general linear hypotheses. Although various approximations of noncentral F distribution are suggested, they are troublesome to compute. In this paper, the calculation of noncentral F distribution is applied to the neural network theory, to solve the computation problem. The neural network consists of the multi-layer perceptron structure and learning process has the algorithm of the backpropagation. Using fables and figs, comparisons are made between the results obtained by neural network theory and the Patnaik's values. Regarding of accuracy and calculation, the results by neural network are efficient than the Patnaik's values.

• The Korean Journal of Applied Statistics
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• v.8 no.2
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• pp.109-119
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• 1995

A two sample chi-square test is introduced for testing the equality of the distributions of two populations when observations are subject to random censorship. The statistic is appropriate in testing problems where a two-sided alternative is of interest. Under the null hypothesis, the asymptotic distribution of the statistic is a chi-square distribution. We obtain two types of chi-square statistics ; one as a nonnegative definite quadratic form in difference of observed cell probabilities based on the product-limit estimators, the other one as a summation form. Data pertaining to a cancer chemotheray experiment are examined with these statistics.

• Journal of the Korean Data and Information Science Society
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• v.25 no.6
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• pp.1195-1205
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• 2014

Compared with single design, powers of rank transformed statistic for testing main and interaction effects for $2{\times}2$ factorial in $4{\times}4$ latin square design are rapidly increased as effect size and replication size are increased. In general powers of rank transformed statistic are superior without regard to the diversified effect composition and the type of error distributions as nontesting factors are few and effect size are small. Powers of rank transformed statistic show much higher level than those of parametric statistic in exponential and double exponential distributions. Further powers of rank transformed statistic are very similar with those of parametric statistic in normal and uniform distributions.