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

AbstractA 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 χ2 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

Numerical computation for the exact distribution of Roy's largest root statistic under linear alternative

This paper discusses the computation of exact powers for Roy's test in multivariate analysis of variance~(MANOVA). We derive an exact expression for the largest eigenvalue of a singular noncentral Beta matrix in terms of the product of zonal polynomials. The numerical computation for that distribution is conducted by an algorithm that expands the product of zonal polynomials as a linear combination of zonal polynomials. Furthermore, we provide an exact distribution of the largest eigenvalue in a form that is convenient for numerical calculations under the linear alternative

Chi-square approximation for the distribution of individual eigenvalues of a singular Wishart matrix

This paper discusses the approximate distributions of eigenvalues of a singular Wishart matrix. We give the approximate joint density of eigenvalues by Laplace approximation for the hyper-geometric functions of matrix arguments. Furthermore, we show that the distribution of each eigenvalue can be approximated by the chi-square distribution with varying degrees of freedom when the population eigenvalues are infinitely dispersed. The derived result is applied to testing the equality of eigenvalues in two population

RWC Music Database: Music Genre Database and Musical Instrument Sound Database

This paper describes the design policy and specifications of the RWC Music Database, a copyright-cleared music database (DB) compiled specifically for research purposes. Shared DBs are common in other research fields and have made significant contributions to progress in those fields. The field of music information processing, however, has lacked a common DB of musical pieces or a large-scale DB of musical instrument sounds. We therefore recently constructed the RWC Music Database comprising four original component DBs: the Popular Music Database (100 pieces), Royalty-Free Music Database (15 pieces), Classical Music Database (50 pieces), and Jazz Music Database (50 pieces). In this paper we report the construction of two additional component DBs: the Music Genre Database (100 pieces) and Musical Instrument Sound Database (50 instruments). For all 315 musical pieces, we prepared original audio signals, corresponding standard MIDI files, and text files of lyrics (for songs). For all 50 instruments, we recorded individual sounds at half-tone intervals with several variations of playing styles, dynamics, instrument manufacturers, and musicians. It is our hope that our DB will make a significant contribution to future advances in the field of music information processing