  We introduce a new one-parameter family of divergence measures, called
bounded Bhattacharyya distance (BBD) measures, for quantifying the
dissimilarity between probability distributions. These measures are bounded,
symmetric and positive semi-definite and do not require absolute continuity. In
the asymptotic limit, BBD measure approaches the squared Hellinger distance. A
generalized BBD measure for multiple distributions is also introduced. We prove
an extension of a theorem of Bradt and Karlin for BBD relating Bayes error
probability and divergence ranking. We show that BBD belongs to the class of
generalized Csiszar f-divergence and derive some properties such as curvature
and relation to Fisher Information. For distributions with vector valued
parameters, the curvature matrix is related to the Fisher-Rao metric. We derive
certain inequalities between BBD and well known measures such as Hellinger and
Jensen-Shannon divergence. We also derive bounds on the Bayesian error
probability. We give an application of these measures to the problem of signal
detection where we compare two monochromatic signals buried in white noise and
differing in frequency and amplitude.
