The diagonal natural exponential families (NEFs) on [real]r were defined and classified recently by Bar-Lev et al. (1994). In this paper, we apply explicit formulas for the Mehler kernels of certain bivariate diagonal NEF classes to develop the total positivity properties of these NEFs and the...

Let be a positive Borel measure on ℝ and (, . . . , ; , . . . , ; ) be a generalized hypergeometric series. We define a := (, . . . , ; , . . . , ), as a series of convolution powers of the measure , and we investigate probability distributions which are expressible as generalized...