• Journal of the Korean Data and Information Science Society
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• 제25권1호
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• pp.195-209
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• 2014

In this paper, we derive the estimators of the location parameter and the scale parameter in a logistic distribution based on multiply type-II censored samples by the approximate maximum likelihood estimation method. We use four modified empirical distribution function (EDF) types test for the logistic distribution based on multiply type-II censored samples using proposed approximate maximum likelihood estimators. We also propose the modified normalized sample Lorenz curve plot for the logistic distribution based on multiply type-II censored samples. For each test, Monte Carlo techniques are used to generate the critical values. The powers of these tests are also investigated under several alternative distributions.

• Communications for Statistical Applications and Methods
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• 제28권2호
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• pp.99-118
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• 2021

In this paper, we introduce an extended form of the inverse power Lomax model via Marshall-Olkin approach. We call it the Marshall-Olkin inverse power Lomax (MOIPL) distribution. The four- parameter MOIPL distribution is very flexible which contains some former and new models. Vital properties of the MOIPL distribution are affirmed. Maximum likelihood estimators and approximate confidence intervals are considered under Type I censored samples. Maximum likelihood estimates are evaluated according to simulation study. Bayesian estimators as well as Bayesian credible intervals under symmetric loss function are obtained via Markov chain Monte Carlo (MCMC) approach. Finally, the flexibility of the new model is analyzed by means of two real data sets. It is found that the MOIPL model provides closer fits than some other models based on the selected criteria.

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.193-200
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• 2014

It was recognized by some researchers that the disturbance variance in a censored regression model is frequently underestimated by the maximum likelihood method. This underestimation has implications for the estimation of marginal effects and asymptotic standard errors. For instance, the actual coverage probability of the confidence interval based on a maximum likelihood estimate can be significantly smaller than the nominal confidence level; consequently, a Bayesian estimation is considered to overcome this difficulty. The behaviors of the maximum likelihood and Bayesian estimators of disturbance variance are examined in a fixed effects panel regression model with a limited dependent variable, which is known to have the incidental parameter problem. Behavior under random effect assumption is also investigated.

• Journal of the Korean Data and Information Science Society
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• 제9권2호
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• pp.247-253
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• 1998

영과잉-포아송모형에서 변화시점이 있는 경우, 돌출대립가설에 대한 우도비검정을 이용하여 변화시점의 유 무를 알아보았다. 변화시점에 대한 추정은 최소제곱법을 이용하였고 이를 최우추정법을 이용하기 위한 초기치로 활용하였다. 또한 대립가설에 대한 몇가지 흥미있는 모수들을 적률법을 이용하여 추정하였다. 모의실험을 통하여 이들 추정 량을 비교하였고 결과 변화시점에 대한 추정은 최소제곱법보다는 최우추정법이 바람직하게 나타났고 흥미있는 몇가지 모수들에 대해서는 최우추정량이 적률추정량보다 우수하게 나타났다.

• 응용통계연구
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• 제19권2호
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• pp.349-360
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• 2006

SAS의 PROC MIXED를 사용하면 일반적인 ANOVA 추정량뿐만 아니라 더 많은 장점을 갖는 제한최대우도추정법 또는 최대우도추정법으로 모수들을 추론할 수 있다. 혼합모형에 속하는 불균형중첩오차구조를 갖는 선형회귀모형에서 랜덤효과와 관련된 그룹간 분산의 신뢰 구간과 고정효과에 해당되는 회귀 계수들에 대 한 신뢰구간을 구하기 위하여 세 가지 크기를 갖는 표본에 대하여 PROC MIXED를 사용하였다. 모의실험을 실행한 결과, 대표본인 경우에는 모수들의 신뢰 구간을 구하기 위하여 PROC MIXED를 활용할 수 있지만, 소표본인 경우에는 PROC MIXED를 사용할 경우, 그룹간 분산의 신뢰 구간과 회귀계수 가운데 절편항의 신뢰구간은 주어진 신뢰계수를 지키지 못하는 것을 보인다.

• Communications for Statistical Applications and Methods
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• 제24권4호
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• pp.353-365
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• 2017

In this article, we proposed a new three-parameter distribution called generalized half-logistic Poisson distribution with a failure rate function that can be increasing, decreasing or upside-down bathtub-shaped depending on its parameters. The new model extends the half-logistic Poisson distribution and has exponentiated half-logistic as its limiting distribution. A comprehensive mathematical and statistical treatment of the new distribution is provided. We provide an explicit expression for the $r^{th}$ moment, moment generating function, Shannon entropy and $R{\acute{e}}nyi$ entropy. The model parameter estimation was conducted via a maximum likelihood method; in addition, the existence and uniqueness of maximum likelihood estimations are analyzed under potential conditions. Finally, an application of the new distribution to a real dataset shows the flexibility and potentiality of the proposed distribution.

• Communications for Statistical Applications and Methods
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• 제26권2호
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• pp.131-148
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• 2019

Constant stress partially accelerated life tests are studied according to exponentiated Weibull distribution. Grounded on multiple censoring, the maximum likelihood estimators are determined in connection with unknown distribution parameters and accelerated factor. The confidence intervals of the unknown parameters and acceleration factor are constructed for large sample size. However, it is not possible to obtain the Bayes estimates in plain form, so we apply a Markov chain Monte Carlo method to deal with this issue, which permits us to create a credible interval of the associated parameters. Finally, based on constant stress partially accelerated life tests scheme with exponentiated Weibull distribution under multiple censoring, the illustrative example and the simulation results are used to investigate the maximum likelihood, and Bayesian estimates of the unknown parameters.

• Communications for Statistical Applications and Methods
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• 제12권3호
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• pp.643-652
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• 2005

It has been known that the exponentiated exponential distribution can be used as a possible alternative to the gamma distribution or the Weibull distribution in many situations. But the maximum likelihood method does not admit explicit solutions when the sample is multiply censored. So we derive the approximate maximum likelihood estimators for the location and scale parameters in the exponentiated exponential distribution that are explicit function of order statistics. We also compare the proposed estimators in the sense of the mean squared error for various censored samples.

• 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.

• Journal of the Korean Data and Information Science Society
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• 제23권4호
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• pp.825-832
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• 2012

We propose a novel way of forecasting the market shares of several brands simultaneously in a multiplicative competitive interaction model, which uses kernel regression technique incorporated with kernel machine technique applied in support vector machines and other machine learning techniques. Traditionally, the estimations of the market share attraction model are performed via a maximum likelihood estimation procedure under the assumption that the data are drawn from a normal distribution. The proposed method is shown to be a good candidate for forecasting method of the market share attraction model when normal distribution is not assumed. We apply the proposed method to forecast the market shares of 4 Korean car brands simultaneously and represent better performances than maximum likelihood estimation procedure.