  This paper introduces a new superfamily of divergences that is similar in
spirit to the S-divergence family introduced by Ghosh et al. (2013). This new
family serves as an umbrella that contains the logarithmic power divergence
family (Renyi, 1961; Maji, Chakraborty and Basu 2014) and the logarithmic
density power divergence family (Jones et al., 2001) as special cases. Various
properties of this new family and the corresponding minimum distance procedures
are discussed with particular emphasis on the robustness issue; these
properties are demonstrated through simulation studies. In particular the
method demonstrates the limitation of the first order influence function in
assessing the robustness of the corresponding minimum distance procedures.
