On bounds in Poisson approximation for distributions of independent negative-binomial distributed random variables
Abstract
Using the Stein–Chen method some upper bounds in Poisson approximation for distributions of row-wise triangular arrays of independent negative-binomial distributed random variables are established in this note.
Some Results on Approximation for Distributions of Random Sums by Poisson Distribution
The main purpose of this paper is to investigate the bounds in Poisson approximation of the distributions for random sums by Poisson distribution via a probability distance based on linear operator introduced by Rényi. Some Le Cam type bounds for distributions of random sums of row-wise independent Poisson-binomial distributed and negative-binomial distributed random variables are obtained.
Estimates in Total Variation for Convolutions of Compound Distributions
Combining Le Cam's operator approach with Bergström's identity, estimates are obtained for convolutions of compound measures. The results are exemplified by consideration of asymptotic expansions for Compound Poisson approximation in Le Cam's theorem, approximation of nearly homogeneous portfolios and convergence to Compound Poisson laws.