• Journal of the Korean Data and Information Science Society
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• 제24권4호
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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.

• Communications for Statistical Applications and Methods
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• 제18권4호
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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.

• 한국지형학회지
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• 제25권2호
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• pp.1-14
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• 2018

The main objective of this paper is to classify properties of the locational environment for each debris type by calculating likelihood ratio based on the correlation between the distributions for each type of debris landform. A total of 8 thematic maps, like as elevation, slope, aspect, curvature, topographic wetness index (TWI), soil drainage, geology, and landcover including with GIS spatial information generally used in this type of debris landform analysis. The results of this study showed that the block stream had a high likelihood ratio compared to talus in areas with relatively high elevation; and concerning slope, the block stream had a high likelihood ratio in a relatively low region than talus. Concerning aspect, a clear correlation could not be analyzed for each debristype, and concerning curvature, the block stream displayed a developed slope on the more concave valley than the talus. Analysis concerning TWI, the block stream displayed a higher likelihood ratio in wider sections than talus, and concerning soil drainage, the talus and block stream both displayed a high likelihood ratio in regions with well-drained soil. The talus displayed a high likelihood ratio in the order of metamorphic rocks, sedimentary rocks, and granite, while the block stream displayed a high likelihood ratio in the order of volcanic rocks, granite, and sedimentary rocks. In addition, concerning landcover, the likelihood ratio had the most concentrated distributed compared to natural bare land only concerning talus. Based on the likelihood ratio result, it can be used as basic data for extracting the possible areas of distribution for each debris type through the GIS spatial integration method.

• Journal of the Korean Data and Information Science Society
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• 제19권4호
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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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• 제23권6호
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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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• 제25권1호
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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.

• 대한음성학회지:말소리
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• 제51호
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• pp.71-84
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• 2004

In this paper, we propose the automatic speech database verification method(or called automatic verification) based on confidence measure for a large speech database. This method verifies the consistency between given transcription and speech using the confidence measure. The automatic verification process consists of two stages : the word-level likelihood computation stage and multi-level likelihood ratio computation stage. In the word-level likelihood computation stage, we calculate the word-level likelihood using the viterbi decoding algorithm and make the segment information. In the multi-level likelihood ratio computation stage, we calculate the word-level and the phone-level likelihood ratio based on confidence measure with anti-phone model. By automatic verification, we have achieved about 61% error reduction. And also we can reduce the verification time from 1 month in manual to 1-2 days in automatic.

• Journal of the Korean Data and Information Science Society
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• 제20권3호
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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.

• Communications for Statistical Applications and Methods
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• 제12권2호
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• pp.473-481
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• 2005

The testing problem for sphericity structure of the covariance matrix in a multivariate normal distribution is introduced when there is a sample with 2-step monotone missing data pattern. The maximum likelihood method is described to estimate the parameters on the basis of the sample. Using these estimates, the likelihood ratio criterion for testing sphericity is derived.

• Journal of the Korean Data and Information Science Society
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• 제23권1호
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• pp.89-98
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• 2012

이 논문에서는 두 개의 Maxwell분포의 모수들의 동질성을 모수비에 근거하여 검정하는 근사통계량을 제안한다. Maxwell분포의 모수비에 대한 추정량이 복잡하여 정확한 분포를 유도하기는 매우 어렵다. 이러한 문제를 해결하기 위한 하나의 대안으로 표준정규분포로 근사적으로 수렴하는 통계량을 고려해야 한다. 이 논문에서 제안된 통계량은 표준정규분포로 수렴하며, 표본의 수가 작은 경우에도 사용할 수 있다. 특히, 본 논문에서는 부호화 로그 우도비 통계량과 수정된 부호화 로그 우도비 통계량을 개발한다. 일반적으로, 수정된 부호화 로그 우도비 통계량은 로그 우도비 통계량에 비해 표준정규분포로 수렴하는 속도가 매우 빠르다. 부호화 로그 우도비 통계량은 작은 표본으로도 표준정규분포로 매우 빨리 수렴한다. 제안된 통계량들의 성질들을 모의실험을 통하여 알아보고, 제안된 통계량을 예제를 통하여 연구한다.