• Communications for Statistical Applications and Methods
• /
• 제23권3호
• /
• pp.241-250
• /
• 2016

In this paper, we consider statistical inferences on the estimation of the parameters of a Weibull distribution when data are randomly censored. Maximum likelihood estimators (MLEs) and approximate MLEs are derived to estimate the parameters. We consider two cases for the censoring model: the assumption that the censoring distribution does not involve any parameters of interest and a censoring distribution that follows a Weibull distribution. A simulation study is conducted to compare the performances of the estimators. The result shows that the MLEs and the approximate MLEs are similar in terms of biases and mean square errors; in addition, the assumption of the censoring model has a strong influence on the estimation of scale parameter.

• Communications for Statistical Applications and Methods
• /
• 제25권6호
• /
• pp.647-658
• /
• 2018

In this paper, we study statistical inferences on the maximum likelihood estimation of a normal distribution when data are randomly censored. Likelihood equations are derived assuming that the censoring distribution does not involve any parameters of interest. The maximum likelihood estimators (MLEs) of the censored normal distribution do not have an explicit form, and it should be solved in an iterative way. We consider a simple method to derive an explicit form of the approximate MLEs with no iterations by expanding the nonlinear parts of the likelihood equations in Taylor series around some suitable points. The points are closely related to Kaplan-Meier estimators. By using the same method, the observed Fisher information is also approximated to obtain asymptotic variances of the estimators. An illustrative example is presented, and a simulation study is conducted to compare the performances of the estimators. In addition to their explicit form, the approximate MLEs are as efficient as the MLEs in terms of variances.

• 생명과학회지
• /
• 제9권2호
• /
• pp.176-181
• /
• 1999

본 연구는 누에(Bombyx mori)에서 cloning한 BomMAR의 염기서열을 기초로 하여 곤충 MLE(mariner-like ele-ment)의 계통분석을 통한 누에의 분자적 계통 관계를 이해하고자 수행하였다. 전체 10 종의 MLE중에서 15%의 낮은 상동성을 보이는 인간 MLE(Hsmarl)을 제외한 9종의 MLE의 DNA 염기서열을 이용한 UPGMA 분석 결과, BmoMAR을 포함한 10종의 MLE가 세 가지의 subfamily 로 grouping되는 것을 알 수 있었으며, 누에는 genetic distance 0.4332에서 같은 lepidoptera(나비목) 의 H. cecropia, almond moth, webworm 및 microcaddisfly와 함께 grouping 되었다. 따라서 이와 같은 결과는 MLE가 곤충의 계통분석에 유용한 molecular tool이 될 수 있음을 보여준다.

• Journal of the Korean Statistical Society
• /
• 제27권1호
• /
• pp.25-55
• /
• 1998

Maximum likelihood estimates (MLEs) for recursive models of categorical variables are discussed under an EM framework. Since MLEs by EM often depend on the choice of the initial values for MLEs, we explore reasonable rules for selecting the initial values for EM. Simulation results strongly support the proposed rules.

• 응용통계연구
• /
• 제25권6호
• /
• pp.1037-1047
• /
• 2012

The generalized linear mixed model(GLMM) is widely used in fitting categorical responses of clustered data. In the numerical approximation of likelihood function the normality is assumed for the random effects distribution; subsequently, the commercial statistical packages also routinely fit GLMM under this normality assumption. We may also encounter departures from the distributional assumption on the response variable. It would be interesting to investigate the impact on the estimates of parameters under misspecification of distributions; however, there has been limited researche on these topics. We study the sensitivity or robustness of the maximum likelihood estimators(MLEs) of GLMM for counts data when the true underlying distribution is normal, gamma, exponential, and a mixture of two normal distributions. We also consider the effects on the MLEs when we fit Poisson-normal GLMM whereas the outcomes are generated from the negative binomial distribution with overdispersion. Through a small scale Monte Carlo study we check the empirical coverage probabilities of parameters and biases of MLEs of GLMM.

• Journal of the Korean Data and Information Science Society
• /
• 제5권2호
• /
• pp.87-94
• /
• 1994

In this paper, we consider optimum plan to determine stress change times under the three-step stress PALTs, assuming that each test units follows an exponential distribution. The tampered random variable(TRV) model for the three-step stress PALTs setup are introduced, and maximum likelihood estimators(MLEs) of the failure rate and the acceleration factors are obtained. The change times to minimize the generalized asymptotic variance(GAVR) of MLEs of the failure rate and the acceleration factors are proposed for the three-step stress PALTs.

• Communications for Statistical Applications and Methods
• /
• 제20권1호
• /
• pp.29-39
• /
• 2013

This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.

• 응용통계연구
• /
• 제11권1호
• /
• pp.185-192
• /
• 1998

Freund(1961)가 제안한 이변량지수분포는 두 부품으로 이루어진 병렬체계의 상호종속적인 부품의 수명을 해석하는 등에 응용될 수 있어 널리 이용되고 있다. 본 연구에서는 위치모수를 가지는 이변량지수분포를 Freund 모형을 일반화시키는 차원에서 제안하고 모형의 통계적 성질 및 모수에 대한 최우추정량을 구하였다. 또한 최우추정량을 수정하여 편의는 감소시킬 수 있는 새로운 추정량을 제안하였다.

• Communications for Statistical Applications and Methods
• /
• 제23권4호
• /
• pp.269-285
• /
• 2016

In this paper, a simple step-stress accelerated life test (ALT) under progressive type-II censoring is considered. Progressive type-II censoring and accelerated life testing are provided to decrease the lifetime of testing and lower test expenses. The cumulative exposure model is assumed when the lifetime of test units follows an extension of the exponential distribution. Maximum likelihood estimates (MLEs) and Bayes estimates (BEs) of the model parameters are also obtained. In addition, a real dataset is analyzed to illustrate the proposed procedures. Approximate, bootstrap and credible confidence intervals (CIs) of the estimators are then derived. Finally, the accuracy of the MLEs and BEs for the model parameters is investigated through simulation studies.

• Journal of the Korean Data and Information Science Society
• /
• 제23권6호
• /
• pp.1249-1257
• /
• 2012

In this paper, we derive maximum likelihood estimators (MLEs) and approximate MLEs (AMLEs) of the unknown parameters in a generalized half logistic distribution when the data are upper record values. As an illustration, we examine the validity of our estimation using real data and simulated data. Finally, we compare the proposed estimators in the sense of the mean squared error (MSE) through a Monte Carlo simulation for various record values of size.