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

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

2010-10-11

arxiv.org/abs/1010.2066v1

Bernoulli 2010, Vol. 16, No. 2, 561-584

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ209 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ209

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.

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