Measuring mobility with entry and exit events

This paper faces the problem of measuring mobility in a set of individuals evolving with the time among k states, when entry/exit phenomena are considered. Movements among the states are usually reckoned through the corresponding transition Matrix P and mobility is measured by a given index I(P). We propose here a procedure based on the hypothesis that entering/exiting individuals make the mobility respectively increase/decrease. Such procedure exploitsexistingmobilityindicesformeasuringtheIncumbentsmobility,according with their starting state, and weighs the contribute of every state using the information about the corresponding entry/exit rate. The new index is proved to satisfy properties of boundedness, immobility and perfect mobility