Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional $\alpha$-entropy and two kinds of non-extensive conditional $\alpha$-entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain sense, they are complementary to generalized inequalities of Fano type.
Rényi $\alpha $-entropy, non-extensive entropy of degree $\alpha $, error probability, Bayesian problems, functional convexity
94E17, 60E15, 62C10, 39B62