Bernoulli

  • Bernoulli
  • Volume 16, Number 2 (2010), 561-584.

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.

Article information

Source
Bernoulli, Volume 16, Number 2 (2010), 561-584.

Dates
First available in Project Euclid: 25 May 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1274821084

Digital Object Identifier
doi:10.3150/09-BEJ209

Mathematical Reviews number (MathSciNet)
MR2668915

Zentralblatt MATH identifier
1248.60025

Keywords
gamma distribution Laplace transform phase-type distribution uniform distance

Citation

Sangüesa, Carmen. Uniform error bounds for a continuous approximation of non-negative random variables. Bernoulli 16 (2010), no. 2, 561--584. doi:10.3150/09-BEJ209. https://projecteuclid.org/euclid.bj/1274821084


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