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.
On Hilbert's thirteenth problem and related questions
Hilbert's thirteenth problem involves the study of solutions of algebraic equations. The object is to obtain a complexity estimate for an algebraic function. As of now, the problem remains open. There are only a few partial algebraic results in this connection, but at the same time the problem has stimulated a series of studies in the theory of functions with their subsequent applications. The most brilliant result in this cycle is Kolmogorov's theorem on superpositions of continuous functions.