Hiroki Hashiguchi

A MEASURE OF SKEWNESS FOR TESTING DEPARTURES FROM NORMALITY

We propose a new skewness test statistic for normality based on the Pearson measure of skewness. We obtain asymptotic first four moments of the null distribution for this statistic by using a computer algebra system and its normalizing transformation based on the Johnson

Visualizing Similarity among Estimated Melody Sequences from Musical Audio

S_{U}

Calculation of a formal moment generating function by using a differential operator

system. Finally the performance of the proposed statistic is shown by comparing the powers of several skewness test statistics against some alternative hypotheses.

The holonomic gradient method for the distribution function of the largest root of a Wishart matrix

We have developed a music retrieval system that receives a humming query and finds similar audio intervals (segments) in a musical audio database. This system enables a user to retrieve a segment of a desired musical audio signal just by singing its melody. In this paper, we propose a method to summarize the music database through similarity analysis to thereby reduce the retrieval time. The distance of chroma vectors is used as a similarity measure. The key technique for summarization includes, mainly, a statistical smoothing method and a method of discriminant analysis. Practical experiments were conducted using 115 musical audio selections in the RWC popular music database. We report the summarization ratio as about 45%.

Bootstrap nonlinear prediction

A differential form in a formal moment generating function is given by the decomposition of powers in terms of the Hermite polynomials. This paper shows that this differential form for calculating the expectation of normal and @g^2 distributions has the benefit of avoiding divergence for Edgeworth type approximations from the viewpoint of a formal power series ring. A symbolic computational algorithm is also discussed, within the distribution theory of statistics.