ABSTRACT
Let { ( X Q , Zo) : H t O} hc a fanlily of random vectors with (3 having-at least three points, such that for each 8. Xe and Zo have respectively the distl ihtiorrs of the form
where p 1 and p 2 arc 0-finite measures defined oil the Bore1 0-field of R a.nd XI and X2 are real Iunctions on O with X L also as a onc-to-one function. Motiwt,ctl by the link hetweell the (L-uninlodality property arid thc survival distribution of a certain type iu a clanlage n~oclcl, we now estit1)lisli the following tl-lcorcrns. These theorems extend the existing characterizations of exponential families based or1 tr-unirnodality.
