On the comparison aspect of the Shannon entropy and the cogentropy

It is claimed that the way the cogentropy defines the probabilities of events, in a certain data set, assuming that only a possibly non-representative subset of the entire set is known, provides better estimates than using those conventionally applied in the Shannon (1948) entropy. In this paper, we apply both entropy measures to estimate the expected uncertainty in the data when the whole data set is known. This expected uncertainty value is nothing but the Shannon entropy when the entire set is known. The effect of the size of the subset on the approximations computed by both entropy measures is investigated. The study takes into consideration the conditional and unconditional cases.