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.
COMPOUND NEGATIVE BINOMIAL APPROXIMATIONS FOR SUMS OF RANDOM VARIABLES
The negative binomial approximations arise in telecommuni cations, network analysis and population genetics, while compound negative binomial approximations arise, for example, in insurance mathematics. In this paper , w first discuss the approximation of the sum of independent, but not identically d istributed, geometric (negative binomial) random variables by a negative binomial dis tribution, using Kerstan’s method and the method of exponents. The appropriate choices f the parameters of the approximating distributions are also suggested. The ra tes of convergence obtained here improve upon, under certain conditions, some of the kno wn results in the literature. The related Poisson convergence result is also studie d. W then extend Kerstan’s method to the case of compound negative binomial approximat ions and error bounds for the total variation metric are obtained. The approximat on by a suitable finite signed measure is also studied. Some interesting special cases are investigated in detail and a few examples are discussed as well. 2000 AMS Mathematics Subject Classification:Primary: 60E05; Secondary: 62E17, 60F05.
Brainstem Influences on the Cephalic Circulation: Experimental Data From Cat and Monkey of Relevance to the Mechanism of Migraine
SYNOPSIS