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ベータ分布を基礎とする新しいタイプの（疑似）一様乱数生成法について議論する．この方法はベータ分布に従う点列をもとにしていて，これらを並べ替えることで乱数を生成する．本報告は3つの点列の紹介をして，その生成方法と理論的背景に言及する．We discuss a new type of uniform random number generator based on the beta distribution. This method consists of a series of points that follow a beta distribution, and can generate random numbers by rearranging them. In this report, we introduce three point sequences and explains their generation method and theoretical background., 情報科学, Information Sciences, 研究ノート

ベータ分布による新しいタイプの一様乱数の生成方法を提案する．これは，真性一様乱数に似た乱数であるため準一様乱数と呼ぶ．結果としての一様乱数ではなく，統計的性質に基づいて生成されることがこの乱数の主な特徴である．もう１つの特性は，Seeds としての乱数の集合からほぼ無限の乱数を生成できることである．その数値的特性と優位性を，数値実験と疑似乱数としてのメルセンヌ＝ツイスター法と物理乱数の比較によって検証する．, We propose a new type of the uniform random number generation method via a beta distribution. We call it a quasi-uniform random number because it is made up of the statistical properties of true random numbers. Another property is that almost infinite random numbers can be obtained from a typical set of random numbers as seeds. Its superiority and numerical characteristics were verified by numerical experiments and comparison with the Mersenne-Twister method as a pseudo-random number and physical random numbers., 情報科学, Information Sciences, 研究ノート

In the practical design process, uncertainty in the parameters should be appropriately taken into account. For example, earthquakes should be considered as uncertain phenomena. Robust design method is known as an effective design method under such uncertain-ties, where a design is found to be insensitive to environment and other uncontrollable factors. Worst-case design of structures is a populism approach as a robust design method, where the objective function and/or the constraints are assigned to the worst values of the structural responses. However, predicting the exact extremes from small samples is difficult in general. Hence, we have proposed use of the k-th worst value instead of the exact worst value. We can predict and control more accurately the behavior of RS by this approach. We could successfully apply the approach to seismic design problems linking with a prescribed accuracy. Through a numerical example, we show the decision based on the k-th order statistics is closely related to the reliability index under some assumptions. The result indicates a new aspect of the proposed robust design method.