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

Xin Liao, Qian Xiong and Zhichao Weng

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 24, 5930-5947

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.

Date: 2020
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DOI: 10.1080/03610926.2019.1623256

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