16 - Statistical Analysis of a Level Sequence

Abstract

This chapter discusses statistical analysis of a level sequence. To estimate the extent to which a given sequence of levels agrees with the eigenvalues of a random matrix, several statistics are considered in the chapter. A statistic is a quantity that can be computed for the given sequence of levels and whose average and mean square scatter are known from the statistical theory of random matrices. Most popular of these statistics are the number variance and the best straight-line-fit Δ statistic along with the two-point correlation function R2(r) and the nearest neighbor spacing probability density p(0; s). The F statistic has sometimes been used to detect small impurities in an otherwise pure sequence.