A view on weighted exponential entropy and examining some of its features

One of the alternative versions of Shannon entropy is a measure of information which is called exponential entropy. Shannon and exponential entropies depend only on the event probabilities. These measures have also been extended to incorporate a set of weights associated with the events. Such weights may reflect some additional characteristics of the events such as their relative importance. In this paper, Axiomatic derivations and properties of weighted exponential entropy parallel to those achieved for weighted entropy are investigated. The relation between weighted exponential entropy of  X and a strictly monotone and nonnegative function of X has obtained. The generalized weighted entropy and the generalized weighted exponential entropy for continuous random variable have been presented.