Abstract
In this short communication, we extend characterization theorems for distributions based on versions of the Chernoff inequality to the case where the distributions are not necessarily purely discrete or absolutely continuous (in the usual sense) and relate these to Cox's representation for a survivor function in terms of the hazard measure, as presented by Kotz and Shanbhag (1980). (The original version of the representation referred to had appeared in Cox, 1972). Some corollaries of the results giving characteristic properties of certain well-known distributions explicitly are also presented.