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Asymptotic approximations for some distributions of ratios

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Abstract

We give strong large deviation results for some ratio distributions. Then we apply these results to two statistical examples: a ratio distribution with sums of gamma-distributed random variables and another one with sums of \(\chi ^2\)-distributed random variables. We eventually carry out numerical comparisons with a saddlepoint approximation using an indirect Edgeworth expansion and a Lugannani and Rice saddlepoint approximation.

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  1. Univ Paul-Valéry Montpellier 3 and IMAG, Univ Montpellier, CNRS, Montpellier, France

    Cyrille Joutard

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  1. Cyrille Joutard
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Correspondence to Cyrille Joutard.

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Joutard, C. Asymptotic approximations for some distributions of ratios. J. Korean Stat. Soc. 51, 868–883 (2022). https://doi.org/10.1007/s42952-022-00165-5

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