Weight functions and sign regularity

Abstract

We examine the question of how the ranking between different distributions with respect to a one-parameter family of weight functions depend on the parameter. We argue that in this context sign regularity of the family of weight functions is a natural condition to consider. Several classical economical examples are shown to satisfy this condition. We use sign regularity to obtain results on the possible rankings similar to well-known bounds on the number of internal rates of return on an investment project, either in continuous or discrete time.