Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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Estimation for the generalized exponential distribution under progressive type I interval censoring

일반화 지수분포를 따르는 제 1종 구간 중도절단표본에서 모수 추정

  • Cho, Youngseukm (Department of Statistics, Pusan National University) ;
  • Lee, Changsoo (Department of Flight Operation, Kyungwoon University) ;
  • Shin, Hyejung (Department of Flight Operation, Kyungwoon University)
  • 조영석 (부산대학교 통계학과) ;
  • 이창수 (경운대학교 항공운항학과) ;
  • 신혜정 (경운대학교 항공운항학과)
  • Received : 2013.09.10
  • Accepted : 2013.10.11
  • Published : 2013.11.30
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Abstract

There are various parameter estimation methods for the generalized exponential distribution under progressive type I interval censoring. Chen and Lio (2010) studied the parameter estimation method by the maximum likelihood estimation method, mid-point approximation method, expectation maximization algorithm and methods of moments. Among those, mid-point approximation method has the smallest mean square error in the generalized exponential distribution under progressive type I interval censoring. However, this method is difficult to derive closed form of solution for the parameter estimation using by maximum likelihood estimation method. In this paper, we propose two type of approximate maximum likelihood estimate to solve that problem. The simulation results show the obtained estimators have good performance in the sense of the mean square error. And proposed method derive closed form of solution for the parameter estimation from the generalized exponential distribution under progressive type I interval censoring.

일반화 지수분포 (generalized exponential distribution)를 따르는 점진 제 1종 구간 중도절단 (progressive type-I interval censoring) 표본에서 모수 추정은 Chen과 Lio (2010)가 최대우도 추정법 (maximum likelihood estimation), 중간점 근사법 (mid-point approximation method), EM 알고리즘 (expectation maximization algorithm), 적률 추정법 (method of moments estimation; MME)으로 하였으며, 그 방법들 중 평균제곱오차 (mean square error; MSE)가 가장 작은 추정법은 중간점 근사법이다. 하지만 중간점 근사법을 바탕으로 최대우도 추정법을 이용하여 모수를 추정하려고 한다면 모수에 대한 해를 전개할 수 없기 때문에 수치 해석적인 방법을 이용하여 추정하여야 한다. 본 논문에서는 이러한 문제를 해결하기 위해서 근사 최대우도 추정법 (approximate maximum likelihood estimation)을 이용하여 두 종류의 모수를 추정하고, 모의실험을 통하여 수치해석학적인 방법을 이용한 중간점 근사법의 해 (estimate of mid-point approximation method; MP)와 제시한 두 가지 추정량을 평균제곱오차 측면에서 비교한다.

Keywords

References

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