Rank mobility index

In economic geography, the rank mobility index (RMI) is a measure of a city's change in population rank among a group of cities.

Formally


 * $$RMI=\frac{R_1-R_2}{R_1+R_2},$$

where


 * R1 = city's rank at time 1
 * R2 = city's rank at time 2

A RMI value must be between &minus;1 and 1. A RMI of 0 indicates no change.