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.