Moments of convex distribution functions and completely alternating sequences

Abstract

We solve the moment problem for convex distribution functions on $[0,1]$ in terms of completely alternating sequences. This complements a recent solution of this problem by Diaconis and Freedman, and relates this work to the Lévy-Khintchine formula for the Laplace transform of a subordinator, and to regenerative composition structures.

Published in at http://dx.doi.org/10.1214/193940307000000374 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

Cited by in corpus (9)

• Gibbs fragmentation trees
• On generating functions of Hausdorff moment sequences
• Exchangeable exogenous shock models
• On the variance of the number of occupied boxes
• Subordinators which are infinitely divisible w.r.t. time: Construction, properties, and simulation of max-stable sequences and infinitely divisible laws
• Moment problems and boundaries of number triangles
• Exchangeable partitions derived from Markovian coalescents
• Complete monotonicity and bernstein properties of functions are characterized by their restriction on N
• Exchangeable partitions derived from Markovian coalescents with simultaneous multiple collisions