A mixing index based on contact numbers by coordination number sampling was proposed by Akao et al. The contact number is defined as the number of particles which are in contact with a particular particle called a specified particle. Statistically, the contact number mixing index is on the basis of the first moment, mean, in contrast to variance-based indexes such as Lacey's.
Shindo reported the distribution of contact numbers from a binary mixture in an incompletely mixed state. The distribution was derived from a beta-binomial distribution as a conditional one.
This paper extends the distribution of contact numbers for a binary case to that for a multicomponent case. The precison of estimation of the mixing index is theoretically derived and compared with that of reduced binary case. It can be concluded that the best precision is obtained if we select the particles whose population concentration is lowest as specified particles. This conclusion holds whatever the number of components is.