• The Korean Journal of Applied Statistics
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• v.25 no.2
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• pp.311-319
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• 2012

The simplest and the most important distribution in survival analysis is exponential distribution. Koziol and Green (1976) derived Cram$\acute{e}$r-von Mises statistic's randomly censored version based on the Kaplan-Meier product limit estimate of the distribution function; however, it could not be practical for a real data set since the statistic is for testing a simple goodness of fit hypothesis. We generalized it to the composite hypothesis for exponentiality with an unknown scale parameter. We also considered the classical Kolmogorov-Smirnov statistic and generalized it by the exact same way. The two statistics are compared through a simulation study. As a result, we can see that the generalized Koziol-Green statistic has better power in most of the alternative distributions considered.

• 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.

• Journal of the military operations research society of Korea
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• v.6 no.2
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• pp.129-149
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• 1980

In medical follow-up, equipment lifetesting, various military situations, and other fields, one often desires to calculate survival probability as a function of time, p(t). If the observer is able to record the time of occurrence of the event of interest (called a 'death'), then an empirical, non-parametric estimate may simply by obtained from the fraction of survivors after various elapsed times. The estimation is more complicated when the data are truncated, i.e., when the observer loses track of some individuals before death occurs. The product-limit method of Kaplan and Meier is one way of estimating p(t) when the mechanism causing truncation is independent of the mechanism causing death. This paper proposes jackknife estimators of logistic trans-formation and compares it to the product-limit method. A computer simulation is used to generate the times of death and truncation from a variety of assumed distributions.