A new asymptotic representation and inversion method for the Student's t distribution
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Publication:6356370
DOI10.1080/10652469.2021.2007906arXiv2012.09789MaRDI QIDQ6356370
Nico M. Temme, A. Gil, Javier Segura
Publication date: 17 December 2020
Abstract: Some special functions are particularly relevant in applied probability and statistics. For example, the incomplete beta function is the cumulative central beta distribution. In this paper, we consider the inversion of the central Student's- distribution which is a particular case of the central beta distribution. The inversion of this distribution functions is useful in hypothesis testing as well as for generating random samples distributed according to the corresponding probability density function. A new asymptotic representation in terms of the complementary error function, will be one of the important ingredients in our analysis. As we will show, this asymptotic representation is also useful in the computation of the distribution function. We illustrate the performance of all the obtained approximations with numerical examples.
Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Computation of special functions and constants, construction of tables (65D20) Incomplete beta and gamma functions (error functions, probability integral, Fresnel integrals) (33B20) Numerical analysis (65-XX)
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