• Journal of the Korean Data and Information Science Society
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• v.8 no.2
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• pp.231-237
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• 1997

The Koziol-Green(KG) model has become an important topic in industrial life testing. In this paper we suggest MLE of the reliability function for the Weibull distribution under the KG model. Futhermore, we compare Kaplan-Meier estimator, Nelson estimator, Cheng & Chang estimator, and Ebrahimi estimator with proposed estimator for the reliability function under the KG model.

• Journal of the Korean Data and Information Science Society
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• v.25 no.2
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• pp.393-402
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• 2014

The simplest and the most important distribution in survival analysis is the exponential distribution. In this paper, we investigate the influence of the random censorship model on the estimation of the scale parameter of the exponential distribution. The considered random censorship models are Koziol-Green model and the generalized exponential distribution model. Two models have different meanings. Through the simulation study, the averages of the estimated values of the parameter do not show big differences, however the MSE of the estimator tends to be bigger when the supposed model is significantly different from the true model.

• Journal of the Korean Data and Information Science Society
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• v.14 no.4
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• pp.975-982
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• 2003

In this paper we considered the problem of estimating the bivariate survival distribution of the random vector (X, Y) when Y may be subject to random censoring but X is always uncensored. Adapting conditional Koziol-Green model, simplified estimator for bivariate survival function is proposed. We perform simulation to compare the proposed estimator with popular estimators and discussed the performance of it.

• The Korean Journal of Applied Statistics
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• v.24 no.5
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• pp.883-891
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• 2011

For survival data we sometimes want to test a log normality hypothesis that can be changed into normality by transforming the survival data. Hence the Shapiro-Wilk type statistic for normality is generalized to randomly censored data based on the Kaplan-Meier product limit estimate of the distribution function. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version under the simpl hypothesis. These two test statistics are compared through a simulation study. As for the distribution of censoring variables, we consider Koziol and Green (1976)'s model and other similar models. Through the simulation results, we can see that the power of the proposed statistic is higher than that of Koziol-Green statistic and that the proportion of the censored observations (rather than the distribution of censoring variables) has a strong influence on the power of the proposed statistic.

• Communications for Statistical Applications and Methods
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• v.26 no.5
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• pp.431-443
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• 2019

Goodness-of-fit techniques are an important topic in statistical analysis. Censored data occur frequently in survival experiments; therefore, many studies are conducted when data are censored. In this paper we mainly consider test statistics based on the empirical distribution function (EDF) to test normal distributions with unknown location and scale parameters when data are randomly censored. The most famous EDF test statistic is the Kolmogorov-Smirnov; in addition, the quadratic statistics such as the $Cram{\acute{e}}r-von$ Mises and the Anderson-Darling statistic are well known. The $Cram{\acute{e}}r-von$ Mises statistic is generalized to randomly censored cases by Koziol and Green (Biometrika, 63, 465-474, 1976). In this paper, we generalize the Anderson-Darling statistic to randomly censored data using the Kaplan-Meier estimator as it was done by Koziol and Green. A simulation study is conducted under a particular censorship model proposed by Koziol and Green. Through a simulation study, the generalized Anderson-Darling statistic shows the best power against almost all alternatives considered among the three EDF statistics we take into account.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.261-270
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• 2002

In this paper, we demonstrate the more accurate confidence intervals for median survival time under the simple proportional hazard model of Koziol and Green (1976) via the Edgeworth expansion for the distribution of the studentized ACL estimator derived in Jeong (2000). The numerical results show that the intervals, so-called test-based and reflect intervals (Slud et al., 1984), outperform normal approximating method in the small sample sizes and/or heavy censoring.