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Goodness-of fit Tests for the Weibull Distribution Based on the Sample Entropy
강석복,이화정 한국데이터정보과학회 2006 한국데이터정보과학회지 Vol.17 No.1
For Type-II censored sample, we propose three modified entropy estimators based on the Vasieck's estimator, van Es' estimator, and Correa's estimator. We also propose the goodness-of-fit tests of the Weibull distribution based on the modified entropy estimators. We simulate the mean squared errors (MSE) of the proposed entropy estimators and the powers of the proposed tests. We also compare the proposed tests with the modified Kolmogorov-Smirnov and Cramer-von-Mises tests which were proposed by Kang et al. (2003).
Goodness-of-t test for the half logistic distribution based on multiply Type-II censored samples
강석복,조영석,한준태,사공진 한국데이터정보과학회 2010 한국데이터정보과학회지 Vol.21 No.2
In this paper, we develop four modied empirical distribution function (EDF) type tests using approximate maximum likelihood estimators for the half-logistic distribution based on multiply Type-II censored samples. We also propose modied normalized sample Lorenz curve polt and new test statistics. We compare the above test statistics in the sense of the power for various censored samples. We present an example to illustrate this method.
강석복,서정인,김용구 한국데이터정보과학회 2013 한국데이터정보과학회지 Vol.24 No.6
This paper develops maximum likelihood estimators (MLEs) of unknown param-eters in an exponentiated half-logistic distribution based on a progressively type-II censored sample. We obtain approximate confidence intervals for the MLEs by using asymptotic variance and covariance matrices. Using importance sampling, we obtain Bayes estimators and corresponding credible intervals with the highest posterior density and Bayes predictive intervals for unknown parameters based on progressively type-II censored data from an exponentiated half logistic distribution. For illustration pur-poses, we examine the validity of the proposed estimation method by using real and simulated data.
강석복,한준태,서연주,정진아 한국데이터정보과학회 2014 한국데이터정보과학회지 Vol.25 No.4
The inverse Weibull distribution has been proposed as a model in the analysis of life testing data. Also, inverse Weibull distribution has been recently derived as asuitable model to describe degradation phenomena of mechanical components such as the dynamic components (pistons, crankshaft, etc.) of diesel engines. In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the shape parameter in the inverse Weibull distribution under multiply type-II censoring. We also develop four modied empirical distribution function (EDF) type tests for the inverse Weibull or extreme value distribution based on multiply type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new teststatistic.
Estimation of Weibull scale parameter based on multiply type II censored samples
강석복,이화정,한준태 한국데이터정보과학회 2004 한국데이터정보과학회지 Vol.15 No.3
We consider the problem of estimating the scale parameter of the Weibull distribution based on multiply Type-II censored samples. We propose two estimators by using the approximate maximum likelihood estimation method for Weibull and extreme value distributions. The proposed estimators are compared in the sense of the mean squared error.
Estimation for the Power Function Distribution Based on Type-II Censored Samples
강석복,정원태 한국데이터정보과학회 2008 한국데이터정보과학회지 Vol.19 No.4
The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.
A Study on Probability and Statistics Education in High School
강석복,최휘택 한국데이터정보과학회 2006 한국데이터정보과학회지 Vol.17 No.2
In this paper, the probability and statistics education of the 7th high school curriculum is studied. We analyze each unit of probability and statistics in high school textbooks 「Mathematics 10-GA」, 「Mathematics Ⅰ」, and 「Practical Mathematics」, and then research the percentage for the unit of probability and statistics for all textbooks. We also investigate the proportion for the number of students who select each subject of mathematics of the national academic aptitude tests for university admission in 2005 and 2006.
강석복,조영석 한국통계학회 2003 응용통계연구 Vol.16 No.2
소득분배의 가장 대표적인 불평등척도는 Gini index이며, 이것은 통계학자인 Gini가 제안한 지표로서 소득분배 에 관한 분석에서 가장 널리 이용되고 있다. 본 논문에서는 두 원의 호에 의해 Lorenz 곡선을 추정하고 코사인법칙을 이용하여 Gini index를 추정하기 위한 새로운 간편한 방법을 제시하여, 소득분포를 따르는 파레토분포에서모의실험을 통해 Ogwang and Rao (1996)의 추정방법과 평균제곱오차 면에서 비교 분석한다. The Gini index is one of the most commonly used measures of inequality of income distributions. In this paper, the Lorenz curve is estimated by arcs of two optimal circles, and a new simple method to estimate the Gini index is proposed using the law of cosines. We compare the proposed estimator with the estimator proposed by Ogwang and Rao(1996) in terms of the mean squared error(MSE) though Monte Carlo simulation in a Pareto distribution.
NORMALIZED SAMPLE LORENZ CURVE를 이용한 검정력이 높은 정규성 검정
강석복,조영석 한국통계학회 2002 응용통계연구 Vol.15 No.2
통계적분석에서 가장 대표적인 가정이 정규성 가정이므로 데이터의 정규성 검정은 매우 중요하다. 이 논문에서는 정규성 검정을 위해 경제학에서 소득분배의 불균형에 관한 척도로 널리 이용되는 Lorenz curve를 변형한 새로운 플롯과 검정통계량을 제시한다. 그리고 제한한 검정을 W검정 (Shapiro and Wilk (1965)), Lorenz curve를 이용한 TL검정(Kang and Cho (1999))과 몬테칼로 방법을 이용하여 검정력을 비교한다. 제안된 검정이 특별한 대립분포의 경우를 제외하고는 대부분 검정력이 높았다. Because most common assumption is normality in statistical analysis, testing normality is very important. We propose a new plot and test statistic to test for normality based on the modified Lorenz curve that is proved to be a powerful tool to measure the income inequality within a population of income receivers. We also compare the proposed test statistics with the W test (Shapiro and Wilk (1965)), TL test (Kang and Cho (1999)) in terms of the power of test through by Monte Carlo method. The proposed test is more usually powerful than the other tests except some case.