• 제목/요약/키워드: Approximate Maximum Likelihood Estimator

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Goodness-of-fit Test for the Weibull Distribution Based on Multiply Type-II Censored Samples

  • Kang, Suk-Bok;Han, Jun-Tae
    • Communications for Statistical Applications and Methods
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    • 제16권2호
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    • pp.349-361
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    • 2009
  • In this paper, we derive the approximate maximum likelihood estimators of the shape parameter and the scale parameter in a Weibull distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We develop three modified empirical distribution function type tests for the Weibull distribution based on multiply Type-II censored samples. We also propose modified normalized sample Lorenz curve plot and new test statistic.

Estimation for the Generalized Extreme Value Distribution Based on Multiply Type-II Censored Samples

  • Han, Jun-Tae;Kang, Suk-Bok
    • Journal of the Korean Data and Information Science Society
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    • 제18권3호
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    • pp.817-826
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    • 2007
  • In this paper, we derive the approximate maximum likelihood estimators of the scale parameter and the location parameter in a generalized extreme value distribution under multiply Type-II censoring by the approximate maximum likelihood estimation method. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

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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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    • 제9권2호
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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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An Analysis of Record Statistics based on an Exponentiated Gumbel Model

  • Kang, Suk Bok;Seo, Jung In;Kim, Yongku
    • Communications for Statistical Applications and Methods
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    • 제20권5호
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    • pp.405-416
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    • 2013
  • This paper develops a maximum profile likelihood estimator of unknown parameters of the exponentiated Gumbel distribution based on upper record values. We propose an approximate maximum profile likelihood estimator for a scale parameter. In addition, we derive Bayes estimators of unknown parameters of the exponentiated Gumbel distribution using Lindley's approximation under symmetric and asymmetric loss functions. We assess the validity of the proposed method by using real data and compare these estimators based on estimated risk through a Monte Carlo simulation.

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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    • 한국데이터정보과학회 2005년도 추계학술대회
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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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Reliability for Series System in Bivariate Weibull Model under Bivariate Type I Censorship

  • Cho, Jang-Sik;Cho, Kil-Ho
    • Journal of the Korean Data and Information Science Society
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    • 제14권3호
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    • pp.571-578
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    • 2003
  • In this paper, we consider two components system which have bivariate weibull model with bivariate type I censored data. We proposed maximum likelihood estimator and relative frequency estimator for the reliability of series system. Also, we construct approximate confidence intervals for the reliability based on the two proposed estimators. And we present a numerical study.

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Estimation of the exponentiated half-logistic distribution based on multiply Type-I hybrid censoring

  • Jeon, Young Eun;Kang, Suk-Bok
    • Communications for Statistical Applications and Methods
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    • 제27권1호
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    • pp.47-64
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    • 2020
  • In this paper, we derive some estimators of the scale parameter of the exponentiated half-logistic distribution based on the multiply Type-I hybrid censoring scheme. We assume that the shape parameter λ is known. We obtain the maximum likelihood estimator of the scale parameter σ. The scale parameter is estimated by approximating the given likelihood function using two different Taylor series expansions since the likelihood equation is not explicitly solved. We also obtain Bayes estimators using prior distribution. To obtain the Bayes estimators, we use the squared error loss function and general entropy loss function (shape parameter q = -0.5, 1.0). We also derive interval estimation such as the asymptotic confidence interval, the credible interval, and the highest posterior density interval. Finally, we compare the proposed estimators in the sense of the mean squared error through Monte Carlo simulation. The average length of 95% intervals and the corresponding coverage probability are also obtained.

Estimation for Two-Parameter Rayleigh Distribution Based on Multiply Type-II Censored Sample

  • Han, Jun-Tae;Kang, Suk-Bok
    • Journal of the Korean Data and Information Science Society
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    • 제17권4호
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    • pp.1319-1328
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    • 2006
  • For multiply Type-II censored samples from two-parameter Rayleigh distribution, the maximum likelihood method does not admit explicit solutions. In this case, we propose some explicit estimators of the location and scale parameters in the Rayleigh distribution by the approximate maximum likelihood methods. We compare the proposed estimators in the sense of the mean squared error for various censored samples.

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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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    • 제11권1호
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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 for the Power Function Distribution Based on Type- II Censored Samples

  • Kang, Suk-Bok;Jung, Won-Tae
    • Journal of the Korean Data and Information Science Society
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    • 제19권4호
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    • pp.1335-1344
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    • 2008
  • The maximum likelihood method does not admit explicit solutions when the sample is multiply censored and progressive censored. So we shall propose some approximate maximum likelihood estimators (AMLEs) of the scale parameter for the power function distribution based on multiply Type-II censored samples and progressive Type-II censored samples when shape parameter is known. We compare the proposed estimators in the sense of the mean squared error (MSE) through Monte Carlo simulation for various censoring schemes.

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