• The Korean Journal of Applied Statistics
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• v.8 no.1
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• pp.89-104
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• 1995

This paper is concerned with the method of estimating lifetime distributin from field data for products with multiple modes of failure. When product failures occur within warranty period, a manufacturer can obtain failure-record data; failure times, causes of failure, and covariates. Since these data are seriously incomplete for satisfactory inference, that is, only failures occured during warrantly period may be recorded, it is usually necessary to incoporate the failure-record data by taking a supplementary sample of items obtained following up a portion of products that survive warranty time. The log linear function is considered as a model for describing the relation between failure time of a product and covariates. General methods for obtaining pseudo maximum likelihood estimators(PMLEs) for the parameters are outlined and their asymptotic properties are studied, and specific formulas for exponential or Weibull distribution are obtained. Effects of follow-up percentage on the PMLEs are investigated. Extensions to calendar time warranty or calendar and obtaining time warranty are also considered.

• The Korean Journal of Applied Statistics
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• v.27 no.3
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• pp.397-406
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• 2014

The minimum density power divergence estimation has been a popular topic in the field of robust estimation for since Basu et al. (1988). The minimum density power divergence estimator has strong robustness properties with the little loss in asymptotic efficiency relative to the maximum likelihood estimator under model conditions. However, a limitation in applying this estimation method is the algebraic difficulty on an integral involved in an estimation function. This paper considers a minimum density power divergence estimation method with approximated divergence avoiding such difficulty. As an example, we consider the normal-exponential convolution model introduced by Bolstad (2004). The estimated divergence in this case is too complicated; consequently, a Laplace approximation is employed to obtain a manageable form. Simulations and an empirical study show that the minimum density power divergence estimators based on an approximated estimated divergence for the normal-exponential model perform adequately in terms of bias and efficiency.

• Journal of the Korean Data and Information Science Society
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• v.26 no.6
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• pp.1305-1315
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• 2015

Consider the risk score which is a function of a linear score for the classification models. The AUC optimization method can be applied to estimate the coefficients of linear score. These estimates obtained by this AUC approach method are shown to be better than the maximum likelihood estimators using logistic models under the general situation which does not fit the logistic assumptions. In this work, the VUS and HUM approach methods are suggested by extending AUC approach method for more realistic discrimination and prediction worlds. Some simulation results are obtained with both various distributions of thresholds and three kinds of link functions such as logit, complementary log-log and modified logit functions. It is found that coefficient prediction results by using the VUS and HUM approach methods for multiple categorical classification are equivalent to or better than those by using logistic models with some link functions.

• Journal of Life Science
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• v.25 no.5
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• pp.533-538
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• 2015

Four sites and one site were used to analyze fish diversity at the water systems of the Sineun reservoir and the Jeonchon reservoir, respectively. The field experiments were conducted to test the density dependence that could lead to population regulation by artificial inferences and environmental changes. We examined the effects of environmental factors on fish densities using SMATR freeware. It was estimated to be reduced to the density effect at four sites in 2012. Shannon-Weaver indices of the diversity (H’) of the Sineun reservoir were similar to those of the Jeonchon reservoir. Species diversity was in a range of 0.645 to 2.105. The H’ value of the upper region was higher than those of middle and low regions were, and values of richness were lower in downstream than upstream. Using the maximum likelihood solution for the removal estimators of two low regions of the river stations, the estimated migration probabilities from the resident fish to the migrated fish for five species (Cyprinus cuvieri, Carassius auratus, Pseudorasbora parva, Misgurnus mizolepis, and Oryzias latipes) had a mean of 0.623. Especially, migration probabilities from the Jeonchon reservoir to the Sineun reservoir for five species were high (a mean of 0.681). The period of migration was suggested to be about one month because of short geographical distances (50 m). We found no significant difference between the three categories in the distribution of the other four species, indicating the species probability was similar among stations.