On some sampling distributions for skew-normal population

Abstract

The distribution of weighted function of independent skew-normal random variables, which includes the sample mean, is useful in many applications. In this paper, we derive this distribution and study the null distribution of a linear form and a quadratic form. Finally, we discuss some of its applications in control charts, in which the skew-normal model plays a key role.

Keywords:

• independence
• moment-generating function
• quadratic form
• skew-normal distribution
• skew-normal sample mean

AMS 2010 Subject Classifications:

• Primary: 62H10
• Secondary: 62E17

Acknowledgments

The authors are very grateful to the anonymous Associate Editor and referee for the valuable comments and suggestions that have considerably improved this work. Support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 99-2118-M-006-005, NSC 102-2118-M-305-003.