• Communications for Statistical Applications and Methods
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• 제23권3호
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• pp.189-201
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• 2016

In survival analysis, the Nelson-Aalen estimator and Peterson estimator are often used to estimate a cumulative hazard function in randomly right censored data. In this paper, we suggested the smoothing version of the cumulative hazard function estimators using a Bezier curve. We compare them with the existing estimators including a kernel smooth version of the Nelson-Aalen estimator and the Peterson estimator in the sense of mean integrated square error to show through numerical studies that the proposed estimators are better than existing ones. Further, we applied our method to the Cox regression where covariates are used as predictors and suggested a survival function estimation at a given covariate.

• Communications for Statistical Applications and Methods
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• 제26권6호
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• pp.623-633
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• 2019

This paper proposes two distance measures between two cumulative hazard functions that can be obtained by comparing their difference and ratio, respectively. Then we estimate the measures and present goodness of t test statistics. Since the proposed test statistics are expressed in terms of the cumulative hazard functions, we can easily give more weights on earlier (or later) departures in cumulative hazards if we like to place an emphasis on earlier (or later) departures. We also show that these test statistics present comparable performances with other well-known test statistics based on the empirical distribution function for an exponential null distribution. The proposed test statistic is an omnibus test which is applicable to other lots of distributions than an exponential distribution.

• Journal of Advanced Marine Engineering and Technology
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• 제24권2호
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• pp.90-96
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• 2000

The technology of preventive maintenance and corrective maintenance is widely applied to ships in order to maintain the good voyageable condition. One of the most important fields of marine engineering is to seek the maximum availability and to solve the stochastic maintenance problem such that the cost for corrective maintenance is minimized. Accordingly, for the purpose of making the most suitable maintenance schedule which minimizes the expected cost function, this paper suggests the method to grasp the failure characteristics by the ship's maintenance data that are collected from the past. And, suggests the method to estimate the optimal maintenance interval by using the dynamic programming and the cumulative hazard rate function attained from the maintenance data.

• Journal of the Korean Data and Information Science Society
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• 제14권3호
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• pp.561-570
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• 2003

We propose a nonparametric test procedure for checking the proportionality assumption between hazard functions using a functional equation. Because of the involvement of censoring distribution function, we consider the large sample case only and obtain the asymptotic normality of the proposeed test statistic. Then we discuss the rationale of the use of the functional equation, give some examples and compare the performances with Andersen's procedure by computing powers through simulations.

• Communications for Statistical Applications and Methods
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• 제23권6호
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• pp.555-562
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• 2016

Interval censored data often occur in an observational study where the subject is followed periodically. Instead of observing an exact failure time, two inspection times that include it are available. There are several methods to analyze interval censored failure time data (Sun, 2006). However, in the presence of competing risks, few methods have been suggested to estimate covariate effect on interval censored competing risk data. A sub-distribution hazard model is a commonly used regression model because it has one-to-one correspondence with a cumulative incidence function. Alternatively, Klein and Andersen (2005) proposed a pseudo-value approach that directly uses the cumulative incidence function. In this paper, we consider an extension of the pseudo-value approach into the interval censored data to estimate regression coefficients. The pseudo-values generated from the estimated cumulative incidence function then become response variables in a generalized estimating equation. Simulation studies show that the suggested method performs well in several situations and an HIV-AIDS cohort study is analyzed as a real data example.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.45-58
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• 2017

Recently, Sati and Gupta (2015) proposed two measures of uncertainty based on non-extensive entropy, called the dynamic cumulative residual Tsallis entropy (DCRTE) and the empirical cumulative Tsallis entropy. In the present paper, we extend the definition of DCRTE into the bivariate setup and study its properties in the context of reliability theory. We also define a new class of life distributions based on bivariate DCRTE.

• 응용통계연구
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• 제20권2호
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• pp.357-371
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• 2007

경쟁위험(competing risk) 하에서의 누적 발생함수(cumulative incidence function)는 일반적으로 비모수적 방법으로 추정된다. 그러나 관심 있는 원인에 의한 사건이 다른 원인에 의한 사건보다 상대적으로 적게 발생하는 경우에 비모수적 방법으로 추정된 누적발생함수는 이산성으로 인해 다소 정확하지 않게 된다. 이와 같은 경우에 Bryant와 Diagnam(2004)는 관심 있는 원인에 대한 원인특정적 위험함수(cause-specific hazard function)를 모수적으로 모형화하고 다른 원인에 의한 사건은 비모수적으로 추정하는 준모수적 방법을 제안했다. 본 연구에서는 준모수적 누적발생함수 추정량을 재표현하고 와이블분포모형과 대수 정규분포모형으로 확장하였다. 또한 대수 정규분포 원인특정적 위험모형일 경우 누적 발생함수에 대한 비모수적 추정량, 와이블분포 준모수적 추정량과 대수 정규분포 준모수적 추정량의 효율성을 비교하며 준모수적 추정량의 성능과 모형 오설정이 미치는 영향을 살펴보았다.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.753-763
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• 2002

When there is one change-point in the hazard rate model, a change-point estimator with the partial score process is suggested and compared with the previously developed estimators. The limiting distribution of the partial score process we used is a function of the Brownian bridge. Simulation study gives the comparison of change-point estimators.

• Communications for Statistical Applications and Methods
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• 제23권5호
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• pp.399-409
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• 2016

Many of studies have suggested the modifications on Weibull distribution to model the non-monotone hazards. In this paper, we combine two cumulative hazard functions and propose a new modified Weibull distribution function. The newly suggested distribution will be named as a new flexible Weibull distribution. Corresponding hazard function of the proposed distribution shows flexible (monotone or non-monotone) shapes. We study the characteristics of the proposed distribution that includes ageing behavior, moment, and order statistic. We also discuss an estimation method for its parameters. The performance of the proposed distribution is compared with existing modified Weibull distributions using various types of hazard functions. We also use real data example to illustrate the efficiency of the proposed distribution.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.147-160
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• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.