• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1173-1181
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• 2008

In this paper, when the parameter of interest is the shape parameter in Pareto distribution, we develop likelihood based inference for this parameter. Specially, we develop signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic for the shape parameter. It is well-known that as sample size grows, the modified signed log-likelihood ratio statistic converges to standard normal distribution faster than the signed log-likelihood ratio statistic. But the computation of the modified signed log-likelihood statistic is hard or even impossible when the sufficient statistics and the ancillary statistics are not clear. In this case, one can consider an approximation to the modified signed log-likelihood statistic. Specially, when the parameter of interest is informationally orthogonal to the nuisance parameters, we propose the approximate modified signed log-likelihood statistic. Through simulation, we investigate the performances of the proposed statistics with the signed log-likelihood statistic.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.911-918
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• 2013

This study deals with the small sample likelihood based inference for the ratio of two normal variances. The small sample likelihood inference is an approximation method. The signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic, which converge to standard normal distribution, are proposed for the normal variance ratio. Through the simulation study, the coverage probabilities of confidence interval and power of the exact, the signed log-likelihood and the modified signed log-likelihood ratio statistic will be compared. A real data example will be provided.

• Journal of the Korean Statistical Society
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• v.32 no.1
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• pp.33-46
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• 2003

The continual reassessment method (CRM) provides a Bayesian estimation of the maximum tolerated dose (MTD) in phase I clinical trials. The CRM has been proposed as an alternative design of the standard design. The CRM has been modified to improve practical feasibility and, recently, the likelihood approach CRM has been proposed. In this paper we investigate the consistency and asymptotic normality of the modified likelihood approach CRM in which the maximum likelihood estimate is used instead of the posterior mean. Small-sample properties of the consistency is examined using complete enumeration. Both the asymptotic results and their small-sample properties show that the modified CRML outperforms the standard design.

• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.209-217
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• 2001

We obtain the approximate maximum likelihood estimators (AMLEs) for the scale and location parameters $\theta$ and $\mu$ in the three-parameter Weibull distribution based on Type-II censored samples. We also compare the AMLEs with the modified maximum likelihood estimators (MMLEs) in the sense of the mean squared error (MSE) based on complete sample.

• Communications for Statistical Applications and Methods
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• v.16 no.2
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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.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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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.

• Journal of the Korean Data and Information Science Society
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• v.17 no.3
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• pp.963-972
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• 2006

This paper focuses on the likelihood based confidence intervals for two inverse gaussian distributions when the parameter of interest is common scale parameter. Confidence intervals based on signed loglikelihood ratio statistic and modified signed loglikelihood ratio statistics will be compared in small sample through an illustrative simulation study.

• Communications for Statistical Applications and Methods
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• v.15 no.5
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• pp.655-666
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• 2008

Small sample likelihood based inference for the shape parameter of the inverse Gaussian distribution is the purpose of this paper. When shape parameter is of interest, the signed log-likelihood ratio statistic and the modified signed log-likelihood ratio statistic are derived. Hsieh (1990) gave a statistical inference for the shape parameter based on an exact method. Throughout simulation, we will compare the statistical properties of the proposed statistics to the statistic given by Hsieh (1990) in term of confidence interval and power of test. We also discuss a real data example.

• 한국데이터정보과학회:학술대회논문집
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• 2002.06a
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• pp.51-73
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• 2002

Empirical likelihood ratio method is a new technique in nonparametric inference developed by A. Owen (1988, 2001). Sometimes empirical likelihood has difficulties to define itself. As such a case in point, we discuss the way to define a modified empirical likelihood for the location of symmetry using well-known points of symmetry as a side conditions. The side condition of symmetry is defined through a finite subset of the infinite set of constraints. The modified empirical likelihood under symmetry studied in this paper is to construct a constrained parameter space $\theta+$ of distributions imposing known symmetry as side information. We show that the usual asymptotic theory (Wilks theorem) still hold for the empirical likelihood ratio on the constrained parameter space and the asymptotic distribution of the empirical NPMLE of difference of two symmetric points is obtained.

• Journal of the Korean Data and Information Science Society
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• v.19 no.4
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• pp.1441-1448
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• 2008

We propose the modified quantile-quantile (Q-Q) plot using the approximate maximum likelihood estimators and the modified normalized sample Lorenz curve (NSLC) plot for the extreme value distribution based on multiply Type-II censored samples. Using two example data sets, we picture the modified Q-Q plot and the modified NSLC plot.