  We construct inequalities between R\'{e}nyi entropy and the indexes of
coincidence of probability distributions, based on which we obtain improved
state-dependent entropic uncertainty relations for general symmetric
informationally complete positive operator-valued measures (SIC-POVM) and
mutually unbiased measurements (MUM) on finite dimensional systems. We show
that our uncertainty relations for general SIC-POVMs and MUMs can be tight for
sufficiently mixed states, and moreover, comparisons to the numerically optimal
results are made via information diagrams.
