On the asymptotic behaviour of the quantiles in the gamma distribution

TL;DR

This paper investigates how the quantiles of the gamma distribution behave asymptotically as the shape parameter approaches zero, providing insights into their limiting behavior and properties at infinity.

Contribution

It offers new asymptotic analysis of gamma distribution quantiles as the shape parameter tends to zero, including remarks on their behavior at infinity.

Findings

Quantiles tend to zero as shape parameter approaches zero.

Behavior at infinity is characterized and discussed.

Asymptotic formulas for quantiles are derived.

Abstract

The asymptotic behaviour of the quantiles in the gamma distribution are investigated as the shape parameter tends to zero. Some remarks about the behaviour at infinity are given.