Dispersion models for geometric sums

Polynomial-geometric Sums

where A(α, k) is the number of permutations of the numbers 1 to α in which exactly k elements are greater than the previous element (the so-called Eulerian numbers), provided we define A(α,−1) to be equal to zero if α > 0 and equal to one if α = 0. Proof. We achieve immediate simplification by linearity, so we only have to deal with one monomial at a time, and in the case of a monomial the mult...

Approximation algorithms for geometric dispersion

Themost basic form of themax-sum dispersion problem (MSD) is as follows: given n points in Rq and an integer k, select a set of k points such that the sum of the pairwise distances within the set is maximal. This is a prominent diversity problem, with wide applications in web search and information retrieval, where one needs to find a small and diverse representative subset of a large dataset. ...

Risk Theory and Geometric Sums

Department of Mathematics Royal Institute of Technology S-10044 Stockholm Sweden email: [email protected] Received October 14, 2002 Vladimir “Volodya” Kalashnikov was a most kind and considerate person. Although we certainly most remember his great personality, we all also knew him as a splendid researcher. I will consider, as mentioned in the title, risk theory and geometric sums which were int...

Dispersion Models for Extremes

We propose extreme value analogues of natural exponential families and exponential dispersionmodels and introduce the hazard slope as an analogue of the variance function. The set of quadraticand power hazard slopes is characterized, and is shown to include well-known distributions such asthe Rayleigh, Gumbel, power, Pareto, logistic, negative exponential, Weibull and Fréchet famili...

Dedekind sums: a combinatorial-geometric viewpoint