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

Carmen Sangüesa

doi:10.3150/09-bej209

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arXiv · 1010.2066

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

Carmen Sangüesa

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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.

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Carmen Sangüesa. 2010-10-11. Uniform error bounds for a continuous approximation of non-negative random variables. https://doi.org/10.3150/09-bej209

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