Theory of the foundation of mathematical statistics to analyze the biological information and its applications

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The research on basic theory of statistical mathematics in the information analysis of bioinformatics, medical sciences, etc. In particular, we consider the problem on sequential experiment of choice, and develop a procedure which maximizes the expected effect in an application plan of 2 treatments in clinical trials. The statistic playing an important role in the inference of two-sample problem follows a non-central distribution in many cases. We analytically derive an approximation formula of a percentage point of the non-central chi-square distribution with the odd degree of freedom, and numerically evaluate the goodness of the approximation of the non-central distribution from the viewpoint of the power and the non-centrality. Further, we derive a higher order approximation formula of the percentage point of the non-central t-statistic, and numerically verify the accuracy of the formula under various distributions.