Optimal guessing under nonextensive framework and associated moment bounds

We consider the problem of guessing realization a random variable but under more general Tsallis’ non-extensive entropic framework rather than classical Maxwell–Boltzman–Gibbs–Shannon framework. both conditional in presence some related side information, and unconditional one where no such side-information is available. For types problem, moment bounds required number guesses are derived; here we use q-normalized expectation place usual (linear) to define moments. These seen be function logarithmic norm entropy measure, recently developed two-parameter generalization Renyi entropy, hence provide their information theoretic interpretation. have also considered case uncertain source distribution derived for corresponding mismatched function. interestingly linked with an important robust statistical divergence family known as relative (α,β)-entropies; similar link discussed between optimum extremes these measures.