We consider in this paper a model of asymmetric power-transformation of response probability explained by linear function of some covariates. This model includes logistic and complementary log-log transformation models as its specific case, so we can use the model to evaluate the appropriateness or the goodness of fit of these models. Then the performances of the asymmetric power-transformation model are evaluated and examined, based on data used in published literatures.And we discuss various issues of diagnoses which may occur in the process of applying the model. Further we consider alternative transformations, and then in comparison with them, we point out the advantages of the asymmetric power-transformation.

Data analysed in medical and biomedical research are often found to have skewed distributions, so transformations are applied to the data in order to render them more tractable by ordinary normal theory analysis. The powernormal distribution, proposed by Goto , Uesaka and Inoue [4], is a distribution which specifies original observations before Box-Cox transformation. In this paper, we mention the maxi mum likelihood method to estimate the parameters of the powernormal distribution, and consider the sampling behaviours of the maximum likelihood estimates. And we show, through simulation experiment , that biases of the transforming parameter, resulted from neglecting the probability proportional constant term, do not seem to cause any troubles in case the aim is to attain approximate normality of the transformed observations, but they do have considerable infuluences on the estimates of the parmeters of nearnormal distribution after the tranformation.

We present a new method for estimating the delay time of a minimum-phase system with delay. It is based on the Hilbert transform relationship between the log magnitude and the phase of a minimum-phase system. An

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