  The past entropy is considered as an uncertainty measure for the past
lifetime distribution. Generating function approach to entropy become popular
in recent time as it generate several well-known entropy measures. In this
paper, we introduce the past entropy-generating function. We study certain
properties of this measure. It is shown that the past entropy-generating
function uniquely determines the distribution. Further, we present
characterizations for some lifetime models using the relationship between
reliability concepts and the past entropy-generating function.
