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.

Keywords:

• Tail properties
• beta-normal distribution
• extreme value distribution

Acknowledgements

We thank the editor in chief and referees for a careful reading of the manuscript and a number of perceptive and useful suggestions which improves it greatly.

Additional information

Funding

The research was supported by the Scientific Research Fund of Sichuan University of Science & Engineering under Grant (2019RC10) and the Opening Project of Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing (grant no. 2018QZJ01).