Rarity of versions

A very important consequence of the fact that the identification system introduced by the catalogue is based on the examination of more than 1300 different thalers is that rarity of the thaler versions can be estimated. The sample is considered large enough to provide a good basis for empirical estimation of the current occurrence frequencies. Let N denote the total number of thalers examined (cca. 1320) and let Ni denote the number of thalers of type "i" within the entire population. The logarithmic rarity value (Ri) of this type is defined as the entire part of the expression

In simple words, the rarity of a type that would form one quarter or more of the entire population is R=0, the rarity of a type that would form less than 1/4 but not less than 1/8 of all the thalers is R=1 and so on, the rarity increases by one if the relative number of the versions decreases to its half. The rarity of a version that is represented by a single piece in the entire population is R=8. There are a few versions which are quoted by other sources but were not found in the population examined. Their rarity is set to R=10.