On lower bounds for Poisson approximation to 2-runs statistic

On the bounds in Poisson approximation for independent geometric distributed random variables

‎The main purpose of this note is to establish some bounds in Poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎Some results related to random sums of independent geometric distributed random variables are also investigated.

Improved Lower Bounds on the Total Variation Distance for the Poisson Approximation

New lower bounds on the total variation distance between the distribution of a sum of independent Bernoulli random variables and the Poisson random variable (with the same mean) are derived via the Chen-Stein method. The new bounds rely on a non-trivial modification of the analysis by Barbour and Hall (1984) which surprisingly gives a significant improvement. A use of the new lower bounds is ad...

on the bounds in poisson approximation for independent geometric distributed random variables

‎the main purpose of this note is to establish some bounds in poisson approximation for row-wise arrays of independent geometric distributed random variables using the operator method‎. ‎some results related to random sums of independent geometric distributed random variables are also investigated.

Lower Bounds for Approximation by Nonlinear Manifolds

which is the precision to which F approximates K. An instance of classical interest is that in which L is C([0, 1]), K is A"—i.e. those functions bounded by one, and whose modulus of continuity is dominated by the modulus of continuity function o>—and F is the family Pn of polynomials of degree n 1. For this case it is known that there are positive constants A and B, independent of to and n, su...

Lower Bounds and Approximation Guarantees