METHODS OF EXTRAPOLATION

INTRODUCTION

With large ancient coinages, so much is missing that a simple die-count is usually not enough to show how many dies were there originally. Thus in the Crepusius die-set with explicit numbering, the die-series remains seriously incomplete, despite the very large samples that have been collected. And with the larger coin-populations of the Principate, even a three-quarter sample of dies is usually far out of reach. The need to extrapolate is widely recognised, but there is much less agreement about how to do this.

Existing methods of extrapolation cannot be discussed individually here. But most are too simple to be capable of modelling the frequencies of Roman coin-types or dies. These frequency-patterns are usually highly skewed, although their skewness varies. Modelling them requires the use of two parameters, which reflect the degree of dispersal as well as the ratio of dies to coins. But most methods applied to coin-evidence rely on the second parameter alone.

The present discussion uses general statistical theory in preference to any of the formulae specially devised for coin-evidence. Roman numismatic data are in fact highly amenable to modelling by a well-known statistical distribution, and modelling by this distribution is considerably more efficient than by most other techniques. The distribution happens to be laborious to calculate, and it is applied here by means of computer programs.

EXTRAPOLATION: METHOD A

The present study deliberately began with the Reka Devnia silver hoard of more than 80,000 coins.