Joint distributional expansions of maxima and minima from skew-normal samples

Abstract

For an independent and identically distributed skew-normal random sequence, the joint distributional asymptotics of normalized partial maximum and minimum are considered. With optimal norming constants, the higher-order expansions of joint distribution and density of normalized maximum and minimum are derived, which deduce convergence rates of joint distribution and density of normalized maximum and minimum to their limits. Numerical analysis is given to compare the accuracy of the actual values with its asymptotics.

Keywords:

• Higher-order expansion
• maximum and minimum
• rate of convergence
• skew-normal distribution

AMS 2000 subject classification:

• Primary 62E20
• 60G70
• Secondary 60F15
• 60F05

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (grant No. 11501113 and No. 11601330) and the Science Foundation of Education Department of Fujian Province (grant No. JA15045).