We propose a simple method of construction of new families of ϕ-divergences. This method called convex standardization is applicable to convex and concave functions ψ(t) twice continuously differentiable in a neighborhood of t=1 with nonzero second derivative at the point t=1. Using this method we introduce several extensions of the LeCam, power, χa and Matusita divergences. The extended families are shown to connect smoothly these divergences with the Kullback divergence or they connect various pairs of these particular divergences themselves. We investigate also the metric properties of divergences from these extended families.
Standard properties of ϕ-divergences of probability measures are widely applied in various areas of information processing. Among the desirable supplementary properties facilitating employment of mathematical methods is the metricity of ϕ-divergences, or the metricity of their powers. This paper extends the previously known family of ϕ-divergences with these properties. The extension consists of a continuum of ϕ-divergences which are squared metric distances and which are mostly new but include also some classical cases like e. g. the Le Cam squared distance. The paper establishes also basic properties of the ϕ-divergences from the extended class including the range of values and the upper and lower bounds attained under fixed total variation.