A general class of univariate skew distributions considering Stein%26apos;s lemma and infinite divisibility

作者：Abtahi A; Behboodian J^*; Sharafi M

来源：Metrika, 2012, 75(2): 193-206.

DOI：10.1007/s00184-010-0322-8

• Skew distribution
• Hidden truncation model
• Moment generating function
• Stein%26apos
• s lemma
• Infinite divisibility

In this article, we consider a general form of univariate skewed distributions. We denote this form by GUS(lambda; h(x)) or GUS with density s(x|lambda, h(x)) = 2f(x)G(lambda h(x)), where f is a symmetric density, G is a symmetric differentiable distribution, and h(x) is an odd function. A special case of this general form, normal case, is derived and denoted by GUSN(lambda; h(x)). Some representations and some main properties of GUS(lambda; h(x)) are studied. The moments of GUSN(lambda; h(x)) and SN(lambda), the known skew normal distribution of Azzalini (1985), are compared and the relationship between them is given. As an application, we use it to construct a new form for skew t-distribution and skew Cauchy distribution. In addition, we extend Stein%26apos;s lemma and study infinite divisibility of GUSN(lambda; h(x)).

• 出版日期2012-2