Mobility as prevailing direction for Transition Matrices

Mobility indices are important tools for summarizing and comparing the dynamics of different samples. A mobility index is defined as a function which assigns a real value $I$ to a given transition matrix . The function $I(P)$, where $P$ is the transition matrix, is chosen to describe a specific type of mobility (e.g. the tendency to leave the current state). In this paper we develop a family of mobility indices capable of embodying information on both the intensity and the prevailing direction of mobility in the sample under study.