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.
A Note on Poisson Approximation for Independent Geometric Random Variables
Let W be a sum of n independent geometric random variables. In 2007, Teerapabolarn and Wongkasem [4] used the Stein-Chen method to give a non-uniform bound in approximating the distribution function of W by the Poisson distribution function with mean λ = E(W )= � n i=1 qip −1 i , where qi =1 −pi. In this paper, a non-uniform bound on the such approximation has been given for the Poisson mean λ = � n=1 qi.
Inhomogeneous Boundary Value Problems for Compressible Navier-Stokes Equations: Well-Posedness and Sensitivity Analysis
In this paper compressible, stationary Navier–Stokes equations are considered. A framework for analysis of such equations is established. In particular, the well-posedness for inhomogeneous boundary value problems of elliptic-hyperbolic type is shown. Analysis is performed for small perturbations of the so-called approximate solutions that take form (1.12). The approximate solutions are determined from Stokes problem (1.11). The small perturbations are given by solutions to (1.13). The uniqueness of solutions for problem (1.13) is proved, and, in addition, the differentiability of solutions with respect to the coefficients of differential operators is shown. The results on the well-posedness of nonlinear problems are interesting on their own and are used to obtain the shape differentiability of the drag functional for incompressible Navier–Stokes equations. The shape gradient of the drag functional is derived in the classical and useful for computations form; an appropriate adjoint state is introduced to ...