Uniform error bounds for a continuous approximation of non-negative random variables

TL;DR

This paper develops uniform error bounds for continuous approximations of non-negative random variables' distribution functions, using gamma-type operators and acceleration techniques, with applications to Erlang and phase-type distributions.

Contribution

It introduces a novel method for uniform error bounds in distribution approximation using gamma-type operators and acceleration techniques.

Findings

Established uniform error bounds for the approximation method.

Applied the bounds to mixtures of Erlang distributions.

Extended results to continuous phase-type distributions.

Abstract

In this work, we deal with approximations for distribution functions of non-negative random variables. More specifically, we construct continuous approximants using an acceleration technique over a well-know inversion formula for Laplace transforms. We give uniform error bounds using a representation of these approximations in terms of gamma-type operators. We apply our results to certain mixtures of Erlang distributions which contain the class of continuous phase-type distributions.