Poisson approximations for telecommunications networks

Poisson approximations for functionals of random trees

We use Poisson approximation techniques for sums of indicator random variables to derive explicit error bounds and central limit theorems for several functionals of random trees. In particular, we consider (i) the number of comparisons for successful and unsuccessful search in a binary search tree and (ii) internode distances in increasing trees. The Poisson approximation setting is shown to be...

Saddlepoint Approximations for Extended Poisson Process Models

The saddlepoint approximation to the probabilities of a general time-homogenous birth process, as derived by Daniels 6 , is revisited. Of interest is the accuracy of the approximation for extended Poisson process models constructed from state-dependent birth processes. Numerical calculations are used to examine the accuracy of the probability approximation for a range of state-dependent models,...

Mobile Telecommunications Protocols for Data Networks Mobile Telecommunications Protocols for Data Networks

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

Poisson approximations on the free Wigner chaos

We prove that an adequately rescaled sequence {Fn} of self-adjoint operators, living inside a xed free Wigner chaos of even order, converges in distribution to a centered free Poisson random variable with rate λ > 0 if and only if φ(F 4 n) − 2φ(F 3 n) → 2λ − λ (where φ is the relevant tracial state). This extends to a free setting some recent limit theorems by Nourdin and Peccati (2009), and pr...