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Sibley and Sempi have constructed metrics on the space of probability distribution functions with the property that weak convergence of a sequence is equivalent to metric convergence. Sibley's work is a modification of Levy's metric, but Sempi's construction is of a different sort. Here we construct a family of metrics having the same convergence properties as Sibley's and Sempi's but which does not appear to be related to theirs in any simple way. Some instances are brought out in which the metrics...
Let μ and ν be two probability measures on the real line and
let c be a lower semicontinuous function on the plane. The mass
transfer problem consists in determining a measure ξ whose
marginals coincide with μ and ν, and whose total cost
∫∫ c(x,y)dξ(x,y) is minimum. In this paper we present
three algorithms to solve numerically this Monge-Kantorovitch problem
when the commodity being shipped is one-dimensional and not
necessarily confined to a bounded interval. We illustrate these
numerical...
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