Small counts in the infinite occupancy scheme

2 5 Se p 20 08 Small counts in the infinite occupancy scheme

The paper is concerned with the classical occupancy scheme with infinitely many boxes, in which n balls are thrown independently into boxes 1, 2,. . ., with probability pj of hitting the box j, where p1 ≥ p2 ≥. .. > 0 and P ∞ j=1 pj = 1. We establish joint normal approximation as n → ∞ for the numbers of boxes containing r1, r2,. .. , rm balls, standardized in the natural way, assuming only tha...

Concentration inequalities in the infinite urn scheme for occupancy counts and the missing mass, with applications

An infinite urn scheme is defined by a probability mass function (pj)j≥1 over positive integers. A random allocation consists of a sample of N independent drawings according to this probability distribution where N may be deterministic or Poisson-distributed. This paper is concerned with occupancy counts, that is with the number of symbols with r or at least r occurrences in the sample, and wit...

Solving infinite horizon optimal control problems of nonlinear interconnected large-scale dynamic systems via a Haar wavelet collocation scheme

We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...

Finite sample properties of the mean occupancy counts and probabilities

For a probability distribution P on an at most countable alphabet A, this article gives finite sample bounds for the expected occupancy counts EKn,r and probabilities EMn,r. Both upper and lower bounds are given in terms of the counting function ν of P . Special attention is given to the case where ν is bounded by a regularly varying function. In this case, it is shown that our general results ...

Modified Noor iterations for infinite family of strict pseudo-contraction mappings