• 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.

• The Mathematical Education
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• v.55 no.2
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• pp.193-208
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• 2016

This study analyzes the likelihood principle and elicits an educational implication. As a result of analysis, this study shows that Frequentist and Bayesian interpret the principle differently by assigning different role to that principle from each other. While frequentist regards the principle as 'the principle forming a basis for statistical inference using the likelihood ratio' through considering the likelihood as a direct tool for statistical inference, Bayesian looks upon the principle as 'the principle providing a basis for statistical inference using the posterior probability' by looking at the likelihood as a means for updating. Despite this distinction between two methods of statistical inference, two statistics schools get clues to compromise in a regard of using frequency prior probability. According to this result, this study suggests the statistics education that is a help to building of students' critical eye by their comparing inferences based on likelihood and posterior probability in the learning and teaching of updating process from frequency prior probability to posterior probability.

• 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 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.

• Proceedings of the Korean Society for Language and Information Conference
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• 2002.02a
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• pp.187-194
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• 2002

In this paper it has been proposed that concession should be analysed as involving scalar implicatures and that an alternative set of situations have to be assumed to account for the the relative nature of likelihood of event occurrence. This paper also claims that the notion of likelihood is the basis of the corresponding pragmatic inference and a universal quantification effect. Unexpectedness, which is conceptually tied to concession, on the other hand involves the same kind of pragmatic inference but presuppose the existence of an alternative set of individuals instead of an alternative set of situations.

• Proceedings of the Korean Statistical Society Conference
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• 2003.05a
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• pp.109-114
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• 2003

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter, which is peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose nonparametric maximum likelihood estimator of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Statistical Society
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• v.33 no.3
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• pp.303-312
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• 2004

The concept of dispersion is intrinsic to the theory and practice of statistics. A formulation of the concept of dispersion can be obtained by comparing the probability of intervals centered about a location parameter. This is the peakedness ordering introduced first by Birnbaum (1948). We consider statistical inference concerning peakedness ordering between two arbitrary distributions. We propose non parametric maximum likelihood estimators of two distributions under peakedness ordering and a likelihood ratio test for equality of dispersion in the sense of peakedness ordering.

• Journal of the Korean Data and Information Science Society
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• v.14 no.2
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• pp.413-428
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• 2003

If a restriction is imposed only to a (proper) subset of parameters of interest, we call it a local restriction. Statistical inference under a local restriction in multinomial setting is studied. The maximum likelihood estimation under a local restriction and likelihood ratio tests for and against a local restriction are discussed. A real data is analyzed for illustrative purpose.

• Journal of applied mathematics & informatics
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• v.13 no.1_2
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• pp.457-470
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• 2003

The comparison of two or more Lorenz curves of Pareto distributions of first kind under arbitrary order restriction is studied. The problem is turned out to be a statistical inference problem concerning scale parameters under order restriction. We assume that the location parameters of Palate distributions are completely unknown. In this paper the maximum likelihood estimation and likelihood ratio tests for and against order restriction are proposed.

• Proceedings of the Korean Information Science Society Conference
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• 2007.06c
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• pp.263-266
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• 2007

This paper discusses the Bayesian statistical inference. This paper discusses the Bayesian inference, MCMC (Markov Chain Monte Carlo) integration, MCMC method, Metropolis-Hastings algorithm, Gibbs sampling, Maximum likelihood estimation, Expectation Maximization algorithm, missing data processing, and BMA (Bayesian Model Averaging). The Bayesian statistical inference is used to process a large amount of data in the areas of biology, medicine, bioengineering, science and engineering, and general data analysis and processing, and provides the important method to draw the optimal inference result. Lastly, this paper discusses the method of principal component analysis. The PCA method is also used for data analysis and inference.