Information of orderα and typeβ

Abstract

Information I_α ^β (Q/P) of orderα and typeβ is introduced and it is shown that for every fixedβ, this information is a monotonic increasing function ofα. It is also shown that information of orderα and type 1 is non-negative when$\sum\limits_{k = 1}^N { q_k } \geqslant \sum\limits_{k = 1}^N { p_k }$, where (q ₁,q ₂ …,q _N) and (p ₁,p ₂, …,p _N) are generalised probability distributions for Q and P respectively.