Some Poisson Approximations Using Compensators
نویسندگان
چکیده
منابع مشابه
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...
متن کاملPoisson 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...
متن کاملSaddlepoint 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,...
متن کاملA New Approach to Poisson Approximations∗
The main purpose of this note is to present a new approach to Poisson Approximations. Some bounds in Poisson Approximations in term of classical Le Cam’s inequalities for various row-wise triangular arrays of independent Poisson-binomial distributed random variables are established via probability distances based on Trotter-Renyi operators. Some analogous results related to random sums in Poiss...
متن کاملSome Generalizations of Poisson Processes
In this paper we make an attempt to review count data models developed so far as generalizations of Poisson process. We consider Winkleman’s gamma count model and the Weibull count model of Mc Shane et al. The fractional generalization of Poisson process by Mainardi et al. is also considered. A Mittag-Leffler count model is developed and studied in detail. Simulation studies are also conducted.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1983
ISSN: 0091-1798
DOI: 10.1214/aop/1176993517