Multivariate arrangement increasing functions with applications in probability and statistics

A real valued function of s vector arguments in Rn is said to be arrangement increasing if the function increases in value as the components of the vector arguments become more similarly arranged. Various examples of arrangement increasing functions are given including many joint multivariate densities, measures of concordance between judges and the permanent of a matrix with nonnegative components. Preservation properties of the class of arrangement increasing functions are examined, and applications are given including useful probabilistic inequalities for linear combinations of exchangeable random vectors.