• Journal of the Korean Statistical Society
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• 제25권3호
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• pp.359-368
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• 1996

The maximum likelihood estimation is discussed for the NLAR model with Laplacian marginals. Since the explicit form of the estimates cannot be obtained due to the complicated nature of the likelihood function we utilize the automatic computer optimization subroutine using a direct search complex algorithm. The conditional least square estimates are used as initial estimates in maximum likelihood procedures. The results of a simulation study for the maximum likelihood estimates of the NLAR(1) and the NLAR(2) models are presented.

• Journal of the Korean Data and Information Science Society
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• 제7권2호
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• pp.263-272
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• 1996

임의의 기계에 대한 수명의 분포는 와이블분포를 하는 경우가 흔하다. 그리고 현실적으로 기계의 수명시간을 검정할 때, 시험시간및 여러 환경적인 제약에 의하여 표본으로 주어진 기계의 수명을 모두 관측하기는 어렵다. 그래서, 본 연구에서는 임의 중단모형 하에서 와이블분포의 모수를 최소제곱법(least squares method)을 이용하여 추정하고 기존의 최대우도추정량(maximum likelihood estimates)과 효율성의 측면에서 비교하고자 한다.

• Communications for Statistical Applications and Methods
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• 제27권1호
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• pp.97-108
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• 2020

This paper compares several methods for estimating parameters of normal inverse Gaussian distribution. Ordinary maximum likelihood estimation and the method of moment estimation often do not work properly due to restrictions on parameters. We examine the performance of adjusted estimation methods along with the ordinary maximum likelihood estimation and the method of moment estimation by simulation and real data application. We also see the effect of the initial value in estimation methods. The simulation results show that the ordinary maximum likelihood estimator is significantly affected by the initial value; in addition, the adjusted estimators have smaller root mean square error than ordinary estimators as well as less impact on the initial value. With real datasets, we obtain similar results to what we see in simulation studies. Based on the results of simulation and real data application, we suggest using adjusted maximum likelihood estimates with adjusted method of moment estimates as initial values to estimate the parameters of normal inverse Gaussian distribution.

• Communications for Statistical Applications and Methods
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• 제28권6호
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• pp.627-641
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• 2021

An asymmetric least squares estimation method has been employed to estimate linear models for percentile regression. An asymmetric maximum likelihood estimation (AMLE) has been developed for the estimation of Poisson percentile linear models. In this study, we propose generalized nonlinear percentile regression using the AMLE, and the use of the parametric bootstrap method to obtain confidence intervals for the estimates of parameters of interest and smoothing functions of estimates. We consider three conditional distributions of response variables given covariates such as normal, exponential, and Poisson for three mean functions with one linear and two nonlinear models in the simulation studies. The proposed method provides reasonable estimates and confidence interval estimates of parameters, and comparable Monte Carlo asymptotic performance along with the sample size and quantiles. We illustrate applications of the proposed method using real-life data from chemical and radiation epidemiological studies.

• Journal of the Korean Data and Information Science Society
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• 제26권2호
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• pp.313-322
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• 2015

본 연구에서는 하나의 균일분포 또는 퇴화분포와 두 개의 이항분포의 혼합분포 모형에 대하여 최우추정법을 소개하며, 제시된 모형에 대하여 시뮬레이션을 통해 최우추정량의 성질을 밝히며, 실험을 통해 얻은 강의 평가 자료에 대하여 퇴화분포를 가지는 혼합분포에 대하여 적용하여 보았다. 특히 퇴화분포는 한국의 문화 특성상 가운데 값을 선호하는 현상을 모형화하는데 유용하게 사용될 수 있음을 보였다.

• International Journal of Reliability and Applications
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• 제9권1호
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• pp.31-52
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• 2008

In this paper generalized version of the geometric distribution is introduced. This distribution can be considered as a two-parameter generalization of the discrete geometric distribution. The main statistical and reliability properties of this distribution are discussed. Two methods of estimation, namely maximum likelihood method and the method of moments are used to estimate the parameters of this distribution. Simulation is utilized to calculate these estimates and to study some of their properties. Also, asymptotic confidence limits are established for the maximum likelihood estimates. Finally, the appropriateness of this new distribution for a set of real data, compared with the geometric distribution, is shown by using the likelihood ratio test and the Kolmogorove-Smirnove test.

• Communications for Statistical Applications and Methods
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• 제23권6호
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• pp.479-496
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• 2016

In this survey, we present a modified inverse moment estimation of parameters and its applications. We use a specific model to demonstrate its principle and how to apply this method in practice. The estimation of unknown parameters is considered. A necessary and sufficient condition for the existence and uniqueness of maximum-likelihood estimates of the parameters is obtained for the classical maximum likelihood estimation. Inverse moment and modified inverse moment estimators are proposed and their properties are studied. Monte Carlo simulations are conducted to compare the performances of these estimators. As far as the biases and mean squared errors are concerned, modified inverse moment estimator works the best in all cases considered for estimating the unknown parameters. Its performance is followed by inverse moment estimator and maximum likelihood estimator, especially for small sample sizes.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.443-451
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• 2005

The studied in this paper is a new algorithm for searching the maximum likelihood estimate(MLE) in which probability density function is not explicitly expressed. Newton-Raphson's root-finding routine and a nonlinear numerical optimization algorithm with constraint (so-called feasible sequential quadratic programming) are used. This algorithm is applied to the Wakeby distribution which is importantly used in hydrology and water resource research for analysis of extreme rainfall. The performance comparison between maximum likelihood estimates and method of L-moment estimates (L-ME) is studied by Monte-carlo simulation. The recommended methods are L-ME for up to 300 observations and MLE for over the sample size, respectively. Methods for speeding up the algorithm and for computing variances of estimates are discussed.

• 한국통신학회논문지
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• 제11권1호
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• pp.73-84
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• 1986

화상이해의 기본적인 특성중의 하나인 edge를 추정하는 statistical 한 방법을 제안하였다. 종래의 edge검출기법은 주로 deterministic한 신호에는 잘 적용되었지만 statistical한 신호에는 만족스러운 결과를 얻을 수 없었다. 본 논문에서는 신호의 statistical 한 성질을 고려한 likelihood함수를 이용하여 결정함수를 구하고, 이것을 최대로 하는 위치를 edge로 선정하는 maximum likelihood edge 검출기법에 대하여 논하였다. 이 기법을 random number generator에 의하여 발생된 통계적인 성질을 갖는 신호에 적용하여 edge가 잘 검출됨을 보였다. 또 이 방법을 통계적인 성질을 갖는 이차원의 화상으로 확장하였을 때에도 정확하게 edge가 검출됨을 알 수 있었다.

• Communications for Statistical Applications and Methods
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• 제16권2호
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• pp.229-238
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• 2009

범주형 자료분석을 위해 고려할 수 있는 모형들은 일반적으로 최우추정에 의하여 적합이 이루어지므로 이상값에 쉽게 영향을 받을 수 있다. 본 연구에서는 분할표 자료에 포함된 이상칸(outlying cell)에 영향을 받지 않는 최대 절삭우도 추정 값(maximum trimmed likelihood estimates)을 얻기 위한 추정 방법을 제안하였다. 제안된 방법은 우도에 의존하여 분할표에 포함된 칸을 제거해나가며 절사우도의 최대값을 찾기 때문에 완전탐색(complete enumeration)에 비해 계산의 양이 매우 적다. 따라서 일반적인 다차원 분할표 자료분석을 위해 쉽게 적용될 수 있다. 실제 자료분석 예를 통해 제안된 추정방법을 설명하였으며, 모의실험을 통해 문제점과 특징을 토론하였다.