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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.
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.
Estimation for the Exponentiated Exponential Distribution Based on Multiply Type-II Censored Samples
강석복,박선미 한국통계학회 2005 Communications for statistical applications and me Vol.12 No.3
It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.
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.
강석복,유세기 嶺南大學校基礎科學硏究所 2002 基礎科學硏究 Vol.22 No.-
In this paper, we prove that the transformed sample Lorenz curve, normalized sample Lorenz curve, and the test statistics for testing of normality based on the normalized sample Lorenz curve and the modified Lorenz curve which were introduced by Kang and Cho (2001a, 2002) are location and scale invariant statistics.