2014/01/07 by Peng Ding · 1 citation
Mathematics · #math.ST #stat.AP #stat.TH #msc:62E15 #msc:62E20 #msc:62F15
paper · pdf · doi:10.1080/00031305.2013.867902
The American Statistician (2014)
arxiv created 2014/01/07 · arxiv updated 2014/01/08
Although it is the generator distribution of the sixth natural exponential family with quadratic variance function, the Hyperbolic-Secant distribution is much less known than other distributions in the exponential families. Its lack of familiarity is due to its isolation from many widely-used statistical models. We fill in the gap by showing three examples naturally generating the Hyperbolic-Secant distribution, including Fisher's analysis of similarity between twins, the Jeffreys' prior for contingency tables, and invalid instrumental variables.