The 2d+4 simple quadratic natural exponential families on R(d)

• 成果类型: Article
• 署名作者: Casalis, M
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1996
• 页码: 1828-1854
• 关键词: variance functions; conjugate priors

摘要

The present paper describes all the natural exponential families on R(d) whose variance function is of the form V(m) = am x m + B(m) + C, with m x m[theta] = [theta,m]m and B tinear in m. There are 2d + 4 types of such families, which are built from particular mixtures of families of Normal, Poisson, gamma, hyperbolic on R and (negative-) multinomial distributions. The proof of this result relies mainly on techniques used in the elementary theory of Lie algebras.