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In this work, we deal with approximations for distribution functions ofnon-negative random variables. More specifically, we construct continuousapproximants using an acceleration technique over a well-know inversion formulafor Laplace transforms. We give uniform error bounds using a representation ofthese approximations in terms of gamma-type operators. We apply our results tocertain mixtures of Erlang distributions which contain the class of continuousphase-type distributions.

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