• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.73-78
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• 2002

In this paper we develop a method for constructing a Bayesian HPD (highest probability density) interval of a ratio of two multivariate normal generalized variances. The method gives a way of comparing two multivariate populations in terms of their dispersion or spread, because the generalized variance is a scalar measure of the overall multivariate scatter. Fully parametric frequentist approaches for the interval is intractable and thus a Bayesian HPD(highest probability densith) interval is pursued using a variant of weighted Monte Carlo (WMC) sampling based approach introduced by Chen and Shao(1999). Necessary theory involved in the method and computation is provided.

• The Korean Journal of Applied Statistics
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• v.23 no.1
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• pp.13-28
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• 2010

Assuming a mixture distribution for credit evaluation studies, we discuss estimating threshold methods to minimize errors that default borrowers are predicted as non defaults or non defaults are regarded as defaults. A method by using statistical hypotheses tests, the most powerful test and generalized likelihood ratio test, for the probability density functions which are defined with the score random variable and the parameter space consisted of only two elements such as the default and non default states is proposed to estimate a threshold. And anther optimal thresholds to maximize classification accuracy measures of the accuracy and the true rate for ROC and CAP curves are estimated as equations related with these probability density functions. Three kinds of optimal thresholds in terms of the hypotheses testing, the accuracy and the true rate are obtained from normal random samples with various means and variances. The sums of the type I and type II errors corresponding to each optimal threshold are obtained and compared. Finally we discuss about their efficiency and derive conclusions.