Tail behavior and extremes of the beta-normal distribution

Abstract

In this paper, the tail properties of the beta-normal distribution and an asymptotic Mills-type ratio are studied. Meanwhile, two applications are presented. The first application obtains the asymptotic behavior of the ratio of probability density functions and the ratio of the tails of the beta-normal and Student’s t distributions. The other one considers the asymptotic distribution of the partial maximum of i.i.d. random variables with the beta-normal distribution.