• Communications for Statistical Applications and Methods
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• v.24 no.1
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• pp.29-41
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• 2017

The estimation problem of expected time to failure of units is studied in a discrete set up. A simple step-stress accelerated life testing is considered with a Type-I censored sample from geometric distribution that is a commonly used distribution to model the lifetime of a device in discrete case. Maximum likelihood estimators as well as the associated distributions are derived. Exact, approximate and bootstrap approaches construct confidence intervals that are compared via a simulation study. Optimal confidence intervals are suggested in view of the expected width and coverage probability criteria. An illustrative example is also presented to explain the results of the paper. Finally, some conclusions are stated.

• Journal of the Korean Data and Information Science Society
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• v.5 no.2
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• pp.59-74
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• 1994

The hazard ratio may be useful as a descriptive measure to compare the hazard experience of a treatment group with that of a control group. In this paper, we propose a kernel estimator of hazard ratio with censored survival data. The uniform consistency and asymptotic normality of the proposed estimator are proved by using counting process approach. In order to assess the performance of the proposed estimator, we compare the kernel estimator with Cox estimator and the generalized rank estimators of hazard ratio in terms of MSE by Monte Carlo simulation.

• Communications for Statistical Applications and Methods
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• v.13 no.1
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• pp.89-99
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• 2006

This article deals with the problem of estimating parameters of Burr Type XII distribution, on the basis of a general progressive Type II censored sample using Bayesian viewpoints. The maximum likelihood estimator does not admit closed form but explicit sharp lower and upper bounds are provided. Assuming squared error loss and linex loss functions, Bayes estimators of the parameter k, the reliability function, and the failure rate function are obtained in closed form. Finally, a simulation study is also included.

• Journal of Korean Society for Quality Management
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• v.12 no.1
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• pp.9-16
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• 1984

We study some estimation of the ${\theta}=P_r$(Y${\theta}$. We consider asymptotic property of estimators and maximum likelihood estimator is compared with unique minimum veriance unbiased estimator in moderate sample size.

• Journal of the Korean Statistical Society
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• v.32 no.2
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• pp.163-174
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• 2003

We propose a test for independence of bivariate censored data under univariate censorship. To do this, we first introduce a process defined by the difference between bivariate survival function estimator proposed by Lin and Ying (1993) and the product of the product-limit estimators (Kaplan and Meier, 1958) for the marginal survival functions, and derive its asymptotic properties under the null hypothesis of independence. We propose a Cramer-von Mises-type test procedure based on the process . We conduct simulation studies to investigate the finite-sample performance of the proposed test and illustrate the proposed test with a real example.

• Communications for Statistical Applications and Methods
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• v.26 no.2
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• pp.131-148
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• 2019

Constant stress partially accelerated life tests are studied according to exponentiated Weibull distribution. Grounded on multiple censoring, the maximum likelihood estimators are determined in connection with unknown distribution parameters and accelerated factor. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample size. However, it is not possible to obtain the Bayes estimates in plain form, so we apply a Markov chain Monte Carlo method to deal with this issue, which permits us to create a credible interval of the associated parameters. Finally, based on constant stress partially accelerated life tests scheme with exponentiated Weibull distribution under multiple censoring, the illustrative example and the simulation results are used to investigate the maximum likelihood, and Bayesian estimates of the unknown parameters.

• Communications for Statistical Applications and Methods
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• v.31 no.4
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• pp.365-375
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• 2024

Diverse methods to evaluate the prediction model of a time to event have been proposed in the context of right censored data where all subjects are subject to be susceptible. A time-dependent AUC (area under curve) measures the predictive ability of a marker based on case group and control one which are varying over time. When a substantial portion of subjects are event-free, a population consists of a susceptible group and a cured one. An uncertain curability of censored subjects makes it difficult to define both case group and control one. In this paper, our goal is to propose a time-dependent AUC for a cure rate model when a censoring distribution is related with covariates. A class of inverse probability of censoring weighted (IPCW) AUC estimators is proposed to adjust the possible sampling bias. We evaluate the finite sample performance of the suggested methods with diverse simulation schemes and the application to the melanoma dataset is presented to compare with other methods.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.533-542
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• 2002

In this paper, a covariate adjusted logrank test is considered for censored paired data under the Cox proportional hazard model. The proposed score test resembles the adjusted logrank test of Tsiatis, Rosner and Tritchler (1985), which is derived from the partial likelihood. The dependence structure for paired data is accommodated into the test statistic by using' sum of square type' variance estimators. Several weight functions are also considered, which produce a class of covariate adjusted weighted logrank tests. Asymptotic normality of the proposed test is established and simulation studies with moderate sample size show the proposed test works well, particularly when there are dependence structure between treatment and covariates.

• Communications for Statistical Applications and Methods
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• v.30 no.4
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• pp.411-421
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• 2023

This paper provides a new estimation equation based on the concept of a minimum distance between the empirical and theoretical distribution functions under the most widely used progressive Type-II censoring scheme. For illustrative purposes, simulated and real datasets from a three-parameter Weibull distribution are analyzed. For comparison, the most popular estimation methods, the maximum likelihood and maximum product of spacings estimation methods, are developed together. In the analysis of simulated datasets, the excellence of the provided estimation method is demonstrated through the degree of the estimation failure of the likelihood-based method, and its validity is demonstrated through the mean squared errors and biases of the estimators obtained from the provided estimation equation. In the analysis of the real dataset, two types of goodness-of-fit tests are performed on whether the observed dataset has the three-parameter Weibull distribution under the progressive Type-II censoring scheme, through which the performance of the new estimation equation provided is examined.

• 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.