POISSON SPACING STATISTICS FOR VALUE SETS OF POLYNOMIALS

If f is a non-constant polynomial with integer coefficients and q is an integer, we may regard f as a map from Z/qZ to Z/qZ. We show that the distribution of the (normalized) spacings between consecutive elements in the image of these maps becomes Poissonian as q tends to infinity along any sequence of square free integers such that the mean spacing modulo q tends to infinity.

STOCHASTIC ORDERINGS BETWEEN SPACINGS OF GENERALIZED ORDER STATISTICS

In this article, we establish stochastic comparisons between normalized spacings of generalized order statistics. These comparisons allow us to extend and unify some results obtained by other authors for ordinary order statistics and record values. Furthermore, we can compare spacings of different models (i.e., between ordinary order statistics and sequential order statistics, record values and Pfeifer's record values, and so forth).