• Title, Summary, Keyword: Approximate maximum likelihood estimator(AMLE)

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AMLE for Normal Distribution under Progressively Censored Samples

  • Kang, Suk-Bok;Cho, Young-Suk
    • Journal of the Korean Data and Information Science Society
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    • v.9 no.2
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    • pp.203-209
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    • 1998
  • By assuming a progressively censored sample, we propose the approximate maximum likelihood estimator (AMLE) of the location nd the scale parameters of the two-parameter normal distribution and obtain the asymptotic variances and covariance of the AMLEs. An example is given to illustrate the methods of estimation discussed in this paper.

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AMLE for the Gamma Distribution under the Type-I censored sample

  • Kang, Suk-Bok;Lee, Hwa-Jung
    • Journal of the Korean Data and Information Science Society
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    • v.11 no.1
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    • pp.57-64
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    • 2000
  • By assuming a Type-I censored sample, we propose the approximate maximum likelihood estimators(AMLE) of the scale and location parameters of the gamma distribution. We compare the proposed estimators with the maximum likelihood estimators(MLE) in the sense of the mean squared errors(MSE) through Monte Carlo method.

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Estimation of the exponential distribution based on multiply Type I hybrid censored sample

  • Lee, Kyeongjun;Sun, Hokeun;Cho, Youngseuk
    • Journal of the Korean Data and Information Science Society
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    • v.25 no.3
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    • pp.633-641
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    • 2014
  • The exponential distibution is one of the most popular distributions in analyzing the lifetime data. In this paper, we propose multiply Type I hybrid censoring. And this paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply Type I hybrid censoring. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator (MLE) of the scale parameter ${\sigma}$ under the proposed multiply Type I hybrid censored samples. We compare the estimators in the sense of the root mean square error (RMSE). The simulation procedure is repeated 10,000 times for the sample size n=20 and 40 and various censored schemes. The $AMLE_{II}$ is better than $AMLE_I$ in the sense of the RMSE.

Approximate MLE for the Scale Parameter of the Weibull Distribution with Type-II Censoring

  • Kang, Suk-Bok;Kim, Mi-Hwa
    • Journal of the Korean Data and Information Science Society
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    • v.5 no.2
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    • pp.19-27
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    • 1994
  • It is known that the maximum likelihood method does not provide explicit estimator for the scale parameter of the Weibull distribution based on Type-II censored samples. In this paper we provide an approximate maximum likelihood estimator (AMLE) of the scale parameter of the Weibull distribution with Type-II censoring. We obtain the asymptotic variance and simulate the values of the bias and the variance of this estimator based on 3000 Monte Carlo runs for n = 10(10)30 and r,s = 0(1)4. We also simulate the absolute biases of the MLE and the proposed AMLE for complete samples. It is found that the absolute bias of the AMLE is smaller than the absolute bias of the MLE.

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Reliability Estimation for the Exponential Distribution under Multiply Type-II Censoring

  • Kang, Suk-Bok;Lee, Sang-Ki;Choi, Hui-Taeg
    • 한국데이터정보과학회:학술대회논문집
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    • pp.13-26
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    • 2005
  • In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and location parameter of the exponential distribution based on multiply Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error for various censored samples. We also obtain the approximate maximum likelihood estimator (AMLE) of the reliability function by using the proposed estimators. And then we compare the proposed estimators in the sense of the mean squared error.

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Estimation for Exponential Distribution under General Progressive Type-II Censored Samples

  • Kang, Suk-Bok;Cho, Young-Suk
    • Journal of the Korean Data and Information Science Society
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    • v.8 no.2
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    • pp.239-245
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    • 1997
  • By assuming a general progressive Type-II censored sample, we propose the minimum risk estimator (MRE) and the approximate maximum likelihood estimator (AMLE) of the scale parameter of the one-parameter exponential distribution. An example is given to illustrate the methods of estimation discussed in this paper.

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Estimation of the Exponential Distributions based on Multiply Progressive Type II Censored Sample

  • Lee, Kyeong-Jun;Park, Chan-Keun;Cho, Young-Seuk
    • Communications for Statistical Applications and Methods
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    • v.19 no.5
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    • pp.697-704
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    • 2012
  • The maximum likelihood(ML) estimation of the scale parameters of an exponential distribution based on progressive Type II censored samples is given. The sample is multiply censored (some middle observations being censored); however, the ML method does not admit explicit solutions. In this paper, we propose multiply progressive Type II censoring. This paper presents the statistical inference on the scale parameter for the exponential distribution when samples are multiply progressive Type II censoring. The scale parameter is estimated by approximate ML methods that use two different Taylor series expansion types ($AMLE_I$, $AMLE_{II}$). We also obtain the maximum likelihood estimator(MLE) of the scale parameter under the proposed multiply progressive Type II censored samples. We compare the estimators in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20 and 40 and various censored schemes. The $AMLE_{II}$ is better than MLE and $AMLE_I$ in the sense of the MSE.

AMLE for the Rayleigh Distribution with Type-II Censoring

  • Kang, Suk-Bok;Cho, Young-Suk;Hwang, Kwang-Mo
    • Journal of the Korean Data and Information Science Society
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    • v.10 no.2
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    • pp.405-413
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    • 1999
  • By assuming a type-II censoring, we propose the approximate maximum likelihood estimators (AMLEs) of the location and the scale parameters of the two-parameter Rayleigh distribution and calculate the asymptotic variances and covariance of the AMLEs.

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Inference Based on Generalized Doubly Type-II Hybrid Censored Sample from a Half Logistic Distribution

  • Lee, Kyeong-Jun;Park, Chan-Keun;Cho, Young-Seuk
    • Communications for Statistical Applications and Methods
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    • v.18 no.5
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    • pp.645-655
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    • 2011
  • Chandrasekar et al. (2004) introduced a generalized Type-II hybrid censoring. In this paper, we propose generalized doubly Type-II hybrid censoring. In addition, this paper presents the statistical inference on the scale parameter for the half logistic distribution when samples are generalized doubly Type-II hybrid censoring. The approximate maximum likelihood(AMLE) method is developed to estimate the unknown parameter. The scale parameter is estimated by the AMLE method using two di erent Taylor series expansion types. We compar the AMLEs in the sense of the mean square error(MSE). The simulation procedure is repeated 10,000 times for the sample size n = 20; 30; 40 and various censored samples. The $AMLE_I$ is better than $AMLE_{II}$ in the sense of the MSE.

Approximate MLE for Rayleigh Distribution in Singly Right Censored Samples

  • Jungsoo Woo;Suk-Bok Kang;Young-Suk Cho;Sangchoon Jeon
    • Communications for Statistical Applications and Methods
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    • v.5 no.1
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    • pp.225-230
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    • 1998
  • By assuming a singly right cenosred sample, we propose the approximate maximum likelihood estimator (AMLE) of the scale parameter of the p-dimensional Rayleigh distribution. We compare the proposed estimator in ·terms of the mean squared error through Monte Carlo methods.

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