Next:Unified EntropyUp:Generalized Entropy Measures

## Entropies of Order 1 and Degree s and Order r and Degree s

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].

21-06-2001
Inder Jeet Taneja
Departamento de Matemática - UFSC
88.040-900 Florianópolis, SC - Brazil