Martín Arevalillo, Jorge2025-03-182025-03-182024Jorge M Arevalillo (2024). On the empirical approximation to quantiles from Lugannani-Rice saddlepoint formula. Statistics & Probability Letters. 209: 110105. https://doi.org/10.1016/j.spl.2024.1101050167-7152https://doi.org/10.1016/j.spl.2024.110105https://hdl.handle.net/20.500.14468/26306The registered version of this article, first published in “Statistics & Probability Letters, vol. 209, 2024", is available online at the publisher's website: Elsevier, https://doi.org/10.1016/j.spl.2024.110105 La versión registrada de este artículo, publicado por primera vez en “Statistics & Probability Letters, vol. 209, 2024", está disponible en línea en el sitio web del editor: Elsevier, https://doi.org/10.1016/j.spl.2024.110105Lugannani–Rice saddlepoint formula approximates the tail probability and the cumulative distribution function of the sample mean of independent and equally distributed variables. This note revisits Lugannani–Rice formula with a proposal for inverting it to approximate the quantile of the distribution empirically. The asymptotic behavior of the empirical approximation is assessed theoretically and its numerical accuracy for finite samples is studied and compared with the normal approximation and the second order Cornish-Fisher expansion by means of a simulation study. The outcomes of the simulation experiment shed light on the limitations of the empirical inversions of saddlepoint formulae to approximate quantileseninfo:eu-repo/semantics/openAccessartículoasymptoticssaddlepoint approximationedgeworthCornish-Fisher