Staircase polygons: moments of diagonal lengths and column heights

We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10-15 July 2005, Queensland, Australi

Total time on test function principal components

A Fourier analytic development of the total time on test function (TTT) provides principal components that are scale free, and which provide criteria for lack of fit. Aggregated values of the squares of these principal components yield a decomposition of the squared coefficient of variation, and a discrete version of the Anderson-Darling type test statistic.Exponential Gini index Goodness of fit Principal component Normalized spacing Total time on test

Subsampling quantile estimator majorization inequalities

A Lorenz partial order majorization inequality is obtained for the Kaigh--Lachenbruch (KL), Harrell--Davis (HD), and Kaigh--Cheng (KC) subsampling quantile estimators developed in Kaigh and Cheng (1991a,b). Bernstein polynomial approximation schemes yield continuous quantile function estimators which are also Lorenz ordered according to their respective inputs.Bernstein polynomial Lorenz curve majorization quantile

Creation or deletion of a drift on a Brownian trajectory

International audienc

Testing whether independent treatment groups have equal medians

L-statistics, Harrell-Davis estimator, bootstrap, kernel density estimates, smoothing,