Hellinger distances and α-entropy in a one-parameter class of density functions

Hellinger distances are considered as measures of distance between density functions, and an inequality concerning different Hellinger distances is proved. Distance measures based on the α-entropy are proposed, and their relationship to a Hellinger distance is shown. Furthermore explicit expressions for the distance measures examined are derived in a one—parameter class of density functions, including Weibull, Gamma, and Maxwell distributions.