• 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.

• 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.

• 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.

• Communications for Statistical Applications and Methods
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• 제15권3호
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• pp.421-427
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• 2008

This paper deals with the problem of testing for the existence of change in mean and estimating the change-point when the data are from the exponential distributions. The likelihood ratio test statistic and Gombay and Horvath (1990) test statistic are compared in a power study when there exists one change-point in the exponential means. Also the change-point estimator using the likelihood ratio and the change-point estimators based on Gombay and Horvath (1990) statistic are compared for their detecting capability via simulation.

• Communications for Statistical Applications and Methods
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• 제15권5호
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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.

• 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.

• Journal of the Korean Data and Information Science Society
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• 제21권2호
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• pp.345-354
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• 2010

The Gamma Distribution is widely used in Engineering and Industrial applications. Estimation of parameters is revisited in the two-parameter Gamma distribution. The parameters are estimated by minimizing the likelihood ratios. A comparative study between the method of moments, the maximum likelihood method, the method of product spacings, and minimization of three different likelihood ratios is performed using simulation. For the scale parameter, the maximum likelihood estimate performs better and for the shape parameter, the product spacings estimate performs better. Among the three likelihood ratio statistics considered, the Anderson-Darling statistic has inferior performance compared to the Cramer-von-Misses statistic and the Kolmogorov-Smirnov statistic.

• 한국국방경영분석학회지
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• 제9권2호
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• pp.39-43
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• 1983

In this paper, we derive the likelihood function for the independent random order statistic whose underlying lifetime distribution is a two parameter Weibull form. For this purpose we first discuss the order statistic which represent a characteristic feature of most life and fatigue tests that they give rise to ordered observations. And, we describe the properties of the underlying Weibull model. The derived likelihood function is essential for establishing the statistical life test plans in the case of Weibull distribution using a likelihood ratio method.

• Communications for Statistical Applications and Methods
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• 제8권2호
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• pp.347-355
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• 2001

We propose a method for detecting influential observations that have a large influence on the likelihood ratio test statistic for the two sets of variables are uncorrelated with one another. For this purpose we derive a local influence measure for the likelihood ratio test statistic under certain perturbation scheme. An illustrative example is given to show the effectiveness of the proposed method on the identification of influential observations.

• Communications for Statistical Applications and Methods
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• 제6권3호
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• pp.939-946
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• 1999

We propose methods for detecting influential observations that have a large influence on the likelihood ratio test statistic for the multivariate Behrens-Fisher problem. For this purpose we derive the influence curve and the derivative influence of the likelihood ratio test statistic. An illustrative example is given to show the effectiveness of the proposed methods on the identification of influential observations.