• Communications for Statistical Applications and Methods
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• v.18 no.4
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• pp.485-493
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• 2011

The proportional likelihood ratio order is an extension of the likelihood ratio order for the non-negative absolutely continuous random variables. In addition, the Lindley distribution has been over looked as a mixture of two exponential distributions due to the popularity of the exponential distribution. In this paper, we first recalled the above concepts and then obtained various properties of the Lindley distribution due to the proportional likelihood ratio order. These results are more general than the likelihood ratio ordering aspects related to this distribution. Finally, we discussed the proportional likelihood ratio ordering in view of the weighted version of the Lindley distribution.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• v.23 no.6
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• pp.563-574
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• 2016

In this study, we propose several simultaneous tests to detect the difference between means and variances for the two-sample problem when the underlying distribution is normal. For this, we apply the likelihood ratio principle and propose a likelihood ratio test. We then consider a union-intersection test after identifying the likelihood statistic, a product of two individual likelihood statistics, to test the individual sub-null hypotheses. By noting that the union-intersection test can be considered a simultaneous test with combination function, also we propose simultaneous tests with combination functions to combine individual tests for each sub-null hypothesis. We apply the permutation principle to obtain the null distributions. We then provide an example to illustrate our proposed procedure and compare the efficiency among the proposed tests through a simulation study. We discuss some interesting features related to the simultaneous test as concluding remarks. Finally we show the expression of the likelihood ratio statistic with a product of two individual likelihood ratio statistics.

• Communications for Statistical Applications and Methods
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• v.25 no.1
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• pp.71-78
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• 2018

In this study, we consider the likelihood ratio test for the covariance matrix of the multivariate normal data. For this, we propose a method for obtaining null distributions of the likelihood ratio statistics by the Monte-Carlo approach when it is difficult to derive the exact null distributions theoretically. Then we compare the performance and precision of distributions obtained by the asymptotic normality and the Monte-Carlo method for the likelihood ratio test through a simulation study. Finally we discuss some interesting features related to the likelihood ratio test for the covariance matrix and the Monte-Carlo method for obtaining null distributions for the likelihood ratio statistics.

• Journal of the Korean Data and Information Science Society
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• v.20 no.3
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• pp.587-592
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• 2009

The most frequent use of the chi-square distribution is in the area of goodness-of-t of a distribution. The likelihood ratio test is a commonly used test statistic as the maximum likelihood estimate in statistical inferences. The recently revised versions of the likelihood ratio test statistics are used in estimating the parameter in the chi-square distribution. The estimates are compared with the commonly used method of moments and the maximum likelihood estimate.

• Journal of the Korean Data and Information Science Society
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• v.15 no.1
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• pp.251-261
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• 2004

The paper focuses primarily on the standard linear multiple regression model where the parameter of interest is a ratio of two regression coefficients. The general model includes the calibration model, the Fieller-Creasy problem, slope-ratio assays, parallel-line assays, and bioequivalence. We provide an orthogonal transformation (cf. Cox and Reid (1987)) of the original parameter vector. Also, we give some remarks on the difficulties associated with likelihood based confidence interval.

• Journal of the Korean Statistical Society
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• v.27 no.2
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• pp.205-220
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• 1998

Dependence concepts for ordered two-way contingency tables have been of considerable interest. We consider a dependence concept which is less restrictive than likelihood ratio dependence and more restrictive than regression dependence. Maximum likelihood estimation of cell probability under this dependence restriction is studied. The likelihood ratio statistics for and against this dependence are proposed and their large sample distributions are derived. A real data is analyzed to illustrate the estimation and testing procedures.

• 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.

• Journal of the Korean Statistical Society
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• v.27 no.3
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• pp.251-264
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• 1998

When the LRT is not feasible, we define quasi-LRT(QLRT) as a modification of the LRT Under some appropriate conditions the QLRT shares Bahadur optimality and Bartlett Adjustability with the LRT. When we can find maximum likelihood estimator under the null parameter space but not under the unrestricted parameter space, our QLRT is Bahadur optimal as is the LRT We suggest the stopping rule of the Newton-Raphson iterations for constructing the QLRT statistics which are Bartlett adjustable.