• Communications for Statistical Applications and Methods
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• 제27권4호
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• pp.469-486
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• 2020

Entropy is an important term in statistical mechanics that was originally defined in the second law of thermodynamics. In this paper, we consider the maximum likelihood estimation (MLE), maximum product spacings estimation (MPSE) and Bayesian estimation of the entropy of an inverse Weibull distribution (InW) under a generalized type I progressive hybrid censoring scheme (GePH). The MLE and MPSE of the entropy cannot be obtained in closed form; therefore, we propose using the Newton-Raphson algorithm to solve it. Further, the Bayesian estimators for the entropy of InW based on squared error loss function (SqL), precautionary loss function (PrL), general entropy loss function (GeL) and linex loss function (LiL) are derived. In addition, we derive the Lindley's approximate method (LiA) of the Bayesian estimates. Monte Carlo simulations are conducted to compare the results among MLE, MPSE, and Bayesian estimators. A real data set based on the GePH is also analyzed for illustrative purposes.

• 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.

• Communications for Statistical Applications and Methods
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• 제5권1호
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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.

• Communications for Statistical Applications and Methods
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• 제18권5호
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• pp.657-666
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• 2011

In this paper, we derive the maximum likelihood estimator(MLE) and some approximate maximum likelihood estimators(AMLEs) of the scale parameter in an exponentiated half logistic distribution based on progressively Type-II censored samples. We compare the proposed estimators in the sense of the mean squared error(MSE) through a Monte Carlo simulation for various censoring schemes. We also obtain the AMLEs of the reliability function.

• Communications for Statistical Applications and Methods
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• 제19권5호
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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.

• Journal of the Korean Data and Information Science Society
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• 제25권6호
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• pp.1581-1589
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• 2014

In this paper, we consider maximum likelihood estimators of the location and scale parameters for the half-logistic distribution when samples are multiply Type I hybrid censored. The scale parameter is estimated by approximate maximum likelihood estimation methods using two different Taylor series expansion types ($\hat{\sigma}_I$, $\hat{\sigma}_{II}$). 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 approximate MLE of the second type is better than that of the first type in the sense of the RMSE. Further an illustrative example with the real data is presented.

• Journal of the Korean Data and Information Science Society
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• 제28권3호
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• pp.659-668
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• 2017

The inverse Weibull distribution (IWD) can be readily applied to a wide range of situations including applications in medicines, reliability and ecology. It is generally known that the lifetimes of test items may not be recorded exactly. In this paper, therefore, we consider the maximum likelihood estimation (MLE) and Bayes estimation of the entropy of a IWD under generalized progressive hybrid censoring (GPHC) scheme. It is observed that the MLE of the entropy cannot be obtained in closed form, so we have to solve two non-linear equations simultaneously. Further, the Bayes estimators for the entropy of IWD based on squared error loss function (SELF), precautionary loss function (PLF), and linex loss function (LLF) are derived. Since the Bayes estimators cannot be obtained in closed form, we derive the Bayes estimates by revoking the Tierney and Kadane approximate method. We carried out Monte Carlo simulations to compare the classical and Bayes estimators. In addition, two real data sets based on GPHC scheme have been also analysed for illustrative purposes.

• Communications for Statistical Applications and Methods
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• 제3권2호
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• pp.175-185
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• 1996

For the Change-point problem in a sequence of binomial variables we consider the maximum likelihood estimator (MLE) of unknown change-point. Its asymptotic distribution is quite limited in the case of binomial variables with different numver of trials at each time point. Hinkley and Hinkley (1970) gives an asymptotic distribution of the MLE for a sequence of Bernoulli random variables. To find the asymptotic distribution a numerical method such as bootstrap can be used. Another concern of our interest in the inference on the change-point and we derive confidence sets based on the liklihood ratio test(LRT). We find approximate confidence sets from the bootstrap distribution and compare the two results through an example.

• Journal of the Korean Data and Information Science Society
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• 제25권3호
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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.

• 응용통계연구
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• 제28권2호
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• pp.281-288
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• 2015

본 연구에서는 혼합모형의 추론을 위한 벌점-최대우도추정량의 빠른 계산절차를 제안하다. 제안된 절차는 벌점-최대우도추정량을 위한 추정방정식에서 헷시안 행렬을 화살촉형태를 지닌 희소행렬을 통하여 근사 시킴으로써 계산속도의 향상을 가져왔다. 두 가지 가상실험을 통하여 제안된 근사식을 사용함으로써 얻게되는 계산시간의 감소와 동시에 이를 위하여 지불하여야 하는 근사오차에 대하여 살펴보았다.