A dataset that contains missing regions is assumed to arise from two or more populations. In order to decompose the data into meaningful component distributions, a normal mixture model can be applied. A problem with this approach is that the estimated parameters are biased by fitting the standard normal mixture model. To correct the bias, a log-likelihood function for missing region probabilities is constructed, and the maximum likelihood estimators of the parameters - i.e. mix-ing proportions, mean vectors, and variance-covariance matrixes - are derived in the context of the EM algorithm. The performance of the model is verified by numerical experiments, and the model is applied to plasma velocity data.

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The Box-Cox transformation, which is a basic method in time series analysis, is not so popular among researchers and practitioners in financial engineering. The well-known Black-Scholes model assumes that stock price exhibits geometric Brownian motion. In other words, log transformed re-turn follows a generalized Wiener process. The log transformation is a special case of the Box-Cox transformation. The goal of this article is to present a valuation method for the option under the assumption that the Box-Cox transformed return process follows a generalized Wiener process. We also empirically examine the effect of the generalization from the log transformation to the Box-Cox transformation in both the stock process itself and the option price based on AIC.
Our result indicates first that, in general, the Box-Cox transformation with optimal parameter is close to the log transformation in a continuing Bull market, while it is not in a Bear market. Second, the result for an equity process based on AIC is mostly reflected in the option price and AIC nearly captures precisely the difference in option prices with respect to the difference in equity process models.
As a practical implication, our option pricing model assuming that the Box-Cox transformed re-turn process follows a generalized Wiener process is able to capture the volatility skew phenomenon often observed in the option market.

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In general, a process starts in an in-control state and then some assignable causes change the process state to be out-of-control. It is worthwhile to utilize serial data in addition to the current data in order to monitor the process state, for which the CUSUM and EWMA control charts are useful. Performance of the CUSUM and EWMA control charts has been investigated under the condition that the process starts in an out-of-control state. However, as mentioned above, a process usually starts in an in-control state. In this paper, we present CUSUM and EWMA control charts based on the Kullback-Leibler information. Then, and investigate their performance under the condition that some assignable causes change the process from the in-control state to an out-of-control state. Because it is also important to discriminate the switchover time of the process state, we propose a discrimination procedure for the process state switchover time based on the information criterion.

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When applying a multivariate statistical method based on the normality assumption to non-normal data, one is tempted to use normal scores for those variates which are apparently non-normal. However, even if all marginal distributions are normal, the joint distribution is not necessarily normal and the method may fail. As a simple counter example, a degenerate bivariate copula which is symmetric about the y-axis, and its normal transformation, the Degenerated Uncorrelated Marginally Normal (DUMgN) distribution, are introduced. Pearson correlation tests of samples from the DUMgN are simulated, and the power of the test is shown to be too poor to be useful. Two other distributions, which are symmetric about both the x and y axes, one is degenerate and the other non-degenerate, are used to further demonstrate the poor performance.

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