Information, measure shifts and distribution metrics

Reflexive shifting of a given distribution, using its own distribution function, can reveal information. The shifts are changes in measure such that the separation of the resulting left and right unit shifted distributions reveals the binary entropy of position, called locational or partition entropy. This can be used for spread and asymmetry functions. Alternatively, summary metrics for distributional asymmetry and spread can be based on the relative strengths of left- and right-hand shifts. Such metrics are applicable even for long tail densities where distributional moments may not exist.