Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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Comparison of Two Parametric Estimators for the Entropy of the Lognormal Distribution

로그정규분포의 엔트로피에 대한 두 모수적 추정량의 비교

  • Choi, Byung-Jin (Department of Applied Information Statistics, Kyonggi University)
  • 최병진 (경기대학교 응용정보통계학과)
  • Received : 20110600
  • Accepted : 20110800
  • Published : 2011.09.30
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Abstract

This paper proposes two parametric entropy estimators, the minimum variance unbiased estimator and the maximum likelihood estimator, for the lognormal distribution for a comparison of the properties of the two estimators. The variances of both estimators are derived. The influence of the bias of the maximum likelihood estimator on estimation is analytically revealed. The distributions of the proposed estimators obtained by the delta approximation method are also presented. Performance comparisons are made with the two estimators. The following observations are made from the results. The MSE efficacy of the minimum variance unbiased estimator appears consistently high and increases rapidly as the sample size and variance, n and ${\sigma}^2$, become simultaneously small. To conclude, the minimum variance unbiased estimator outperforms the maximum likelihood estimator.

본 논문에서는 로그정규분포의 엔트로피에 대한 모수적 추정량으로 최소분산비편향추정량과 최대가능도추정량을 제시하고 성질을 비교한다. 각 추정량의 분산을 유도해서 일치성을 밝히고 최대가능도 추정량의 편향이 추정에 미치는 영향을 분석한다. 델타근사방법을 이용해서 얻은 추정량의 분포를 제시하고 적합도 평가를 통한 유도한 분포의 확증을 위해서 모의실험을 수행한다. 평균제곱오차에 의한 상대적 효율성에 대한 조사를 통해 두 추정량의 성능을 비교한다. 모의실험의 결과에서 최소분산비편향추정량은 최대가능도 추정량보다 더 좋은 효율을 보이는 것으로 나타나며, 특히 표본크기와 분산이 동시에 작아짐에 따라 효율이 점점 높아지게 되어 월등히 나은 성능을 발휘함을 볼 수 있다.

Keywords

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