Sharma and Mittal (1975) [90] introduced
and characterized two entropies called entropy of order
and degree
and entropy of order
and degree
given by

(3.6) 
and

(3.7) 
respectively, for all , where and are real parameters.
Sharma and Mittal's main motivation was to generalize the three entropies, and . With this aim, they arrived at . reduces to and , when and , respectively. reduces to and when and respectively. Also, reduces to Shannon's entropy, H(P), when .
Thus, we see that the entropy of order and degree contain, either as a limiting or as a particular case, the Shannon's entropy, the entropy of order , the entropy of degree , the entropy of kind t, and the entropy of order 1 and degree .
We have presented in the previous subsections seven generalized entropies
having one and/or two scalar parameters. A natural question arises at this
stage, what kind of other generalized entropies exist in the literature.
For a complete list we refer to section 3.6.2 (Taneja, 1989; 1990a) [105],
[106].