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More than 30 measures of entropies have been introduced in the literature on Information theory generalizing Shannon's entropy. These are famous as parametric, trigonometric and weighted entropies. Rényi (1961) [82] for the first time gave the idea of parametric entropy. The idea of trigonometric entropies was initiated by Aczél and Daróczy (1963) [1] . Later Sharma and Taneja (1977) [93]and Sant'anna and Taneja (1985) [85] studied it from different aspects. The idea of weighted entropies started by Belis and Guaisu (1968) [10]. Later Picard (1979) [77] extended it for generalized measures. This chapter mainly deals with the parametric entropies involving one and two scalar parameters. After Rényi (1961) [82], other researchers viz., Havrda and Charvát (1967) [46], Arimoto (1971) , Sharma and Mittal (1975) [90] etc.. interested towards other kinds of expressions generalizing Shannon's entropy. Taneja (1989) [105] unified some of these. In this chapter, we shall study in details the idea of unification of different parametric entropies.

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