Local tail bounds for functions of independent random variables

Local Tail Bounds for Functions of Independent Random Variables

It is shown that functions defined on {0, 1, . . . , r − 1}n satisfying certain conditions of bounded differences that guarantee subgaussian tail behavior also satisfy a much stronger “local” subgaussian property. For self-bounding and configuration functions we derive analogous locally subexponential behavior. The key tool is Talagrand’s (1994) variance inequality for functions defined on the ...

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.

Bounds for Tail Probabilities of Weighted Sums of Independent Gamma Random Variables

The tail probabilities of two weighted sums of independent gamma random variables are compared when the first vector of weights majorizes the second vector of weights. The conjecture that the two cumulative distribution .functions cross exactly once is established in four special cases by means of the variation-diminishing property of totally positive kernels. Bounds are obtained for the locati...

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.

Tail sums of convergent series of independent random variables