![Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5943/TOC-Subject-Sample-2021-Mathematics-Statistics.jpg"})
Abstract
For every continuous random variable with probability density function (pdf) f(x) a corresponding dual pdf f*(x) can be defined in terms of the moment generating function (mgf) or the characteristic function (cf). In this note, formulas for f*(x) are provided for the most applied continuous distributions (27of them). More than ten motivating applications are described. The results give rise to many new distributions that are not known in the current literature.