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In this work in progress, we study the asymptotic behaviour of the$p$-quantile of the Beta distribution, i.e. the quantity $q$ defined implicitlyby $\int_0^q t^{a - 1} (1 - t)^{b - 1} \text{d} t = p B (a, b)$, as a functionof the first parameter $a$. In particular, we derive asymptotic expansions ofand $q$ and its logarithm at $0$ and $\infty$. Moreover, we provide somerelations between Bell and N{\o}rlund Polynomials, a generalisation ofBernoulli numbers. Finally, we provide Maple and Sage algorithms for computingthe terms of the asymptotic expansions.

Asymptotic expansions of the inverse of the Beta distribution