• Journal of the Korean Mathematical Society
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• v.51 no.3
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• pp.609-633
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• 2014

From the ordinary notion of uniformly strong mixing for a sequence of random variables, a new concept called conditionally uniformly strong mixing is proposed and the relation between uniformly strong mixing and conditionally uniformly strong mixing is answered by examples, that is, uniformly strong mixing neither implies nor is implied by conditionally uniformly strong mixing. A couple of equivalent definitions and some of basic properties of conditionally uniformly strong mixing random variables are derived, and several conditional covariance inequalities are obtained. By means of these properties and conditional covariance inequalities, a conditional central limit theorem stated in terms of conditional characteristic functions is established, which is a conditional version of the earlier result under the non-conditional case.

• Journal of the Korean Mathematical Society
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• v.51 no.1
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• pp.1-15
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• 2014

A conditional version of the classical central limit theorem is derived rigorously by using conditional characteristic functions, and a more general version of conditional central limit theorem for the case of conditionally independent but not necessarily conditionally identically distributed random variables is established. These are done anticipating that the field of conditional limit theory will prove to be of significant applicability.

• Journal of the Korean Statistical Society
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• v.23 no.1
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• pp.89-102
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• 1994

A new method for approximating the average run length (ARL) of cumulative sum (CUSUM) chart is proposed. This method uses the conditional expectation for the test statistic before the stopping time and its asymptotic conditional density function. The values obtained by this method are compared with some other methods in normal and exponential case.

• Journal of Korean Institute of Industrial Engineers
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• v.41 no.1
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• pp.10-16
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• 2015

In this study, we suggest a method to predict probability distribution of a new customer's degree of loyalty using C-CRF that reflects the RFM score and similarity to the neighbors of the customer. An RFM score prediction model is introduced to construct the first feature function of C-CRF. Integrating demographical similarity, purchasing characteristic similarity and purchase history similarity, we make a unified similarity variable to configure the second feature function of C-CRF. Then parameters of each feature function are estimated and we train our C-CRF model by training data set and suggest a probabilistic distribution to estimate a new customer's degree of loyalty. An example is provided to illustrate our model.