Statistical estimation of the number of dies
The study of coin dies is essential for understanding coin production at ancient mints. However, determining the total number of dies used to strike the surviving coins of a particular type can sometimes be a difficult undertaking because of the large volume of material collected or its poor state of preservation. A considerable number of die studies have been published on Iberian coinage, particularly in monographs devoted to individual mints. Nevertheless, many mints still lack studies of this kind, creating an opportunity to apply statistical methods to estimate the total number of dies used in coin production during the Iberian period.
The statistical application developed by monedaiberica.org provides an estimate of the number of dies used in coin production, both overall and for individual types. The model implemented in this tool is based on data from 208 coin types issued by ten mints that have been examined through die studies published in articles and monographs (Ripollès 1988; 2007; 2017; Ripollès and Chevillon 2013; 2020; Ripollès and Llorens 2002; Gomis 1995; 1996; Abascal and Ripollès 2000; Gozalbes 2009; Sinner 2017), together with the number of coins documented in monedaiberica.org.
Based on this information, the following relationship has been established:
Estimated number of dies = e^α · (Number of coins)^β
The use of this model is appropriate because increasing the coin sample raises the probability of identifying new dies. The result varies depending on whether obverse or reverse dies are being estimated (see the statistical development of the model in the attached document). This is because the model is fitted to values drawn from the scholarly literature and, in coin production, the working lives of obverse and reverse dies differ; in general, obverse dies are represented in smaller numbers than reverse dies.
The model produces point estimates -a single value for each type- which have been supplemented with bootstrapconfidence intervals to quantify the uncertainty associated with each estimate.
The result of the statistical calculation is dynamic: it is updated according to the number of coins recorded for each type in the monedaiberica.org catalogue. Consequently, whenever new specimens are added, both the estimated value and its associated confidence interval are updated automatically.
The results should be understood as approximations conditioned by the initial data. It should be noted that, for types represented by between one and seven coins, the model does not consistently capture the trend in the number of dies. In such cases, the estimate is set at one obverse die and one reverse die. This is because the initial sample of 208 types used to construct the statistical model included widely varying coin-to-die ratios, generally either few coins and many dies or few coins and few dies, and these values were therefore excluded from the analysis.
The implementation of this tool demonstrates how statistics can advance the study of Iberian coin production by providing results -even if only approximate- that would often be difficult to obtain using traditional counting methods. It is hoped that future numismatic research will, over time, validate the proposed estimates.
The statistical application developed by monedaiberica.org provides an estimate of the number of dies used in coin production, both overall and for individual types. The model implemented in this tool is based on data from 208 coin types issued by ten mints that have been examined through die studies published in articles and monographs (Ripollès 1988; 2007; 2017; Ripollès and Chevillon 2013; 2020; Ripollès and Llorens 2002; Gomis 1995; 1996; Abascal and Ripollès 2000; Gozalbes 2009; Sinner 2017), together with the number of coins documented in monedaiberica.org.
Based on this information, the following relationship has been established:
Estimated number of dies = e^α · (Number of coins)^β
The use of this model is appropriate because increasing the coin sample raises the probability of identifying new dies. The result varies depending on whether obverse or reverse dies are being estimated (see the statistical development of the model in the attached document). This is because the model is fitted to values drawn from the scholarly literature and, in coin production, the working lives of obverse and reverse dies differ; in general, obverse dies are represented in smaller numbers than reverse dies.
The model produces point estimates -a single value for each type- which have been supplemented with bootstrapconfidence intervals to quantify the uncertainty associated with each estimate.
The result of the statistical calculation is dynamic: it is updated according to the number of coins recorded for each type in the monedaiberica.org catalogue. Consequently, whenever new specimens are added, both the estimated value and its associated confidence interval are updated automatically.
The results should be understood as approximations conditioned by the initial data. It should be noted that, for types represented by between one and seven coins, the model does not consistently capture the trend in the number of dies. In such cases, the estimate is set at one obverse die and one reverse die. This is because the initial sample of 208 types used to construct the statistical model included widely varying coin-to-die ratios, generally either few coins and many dies or few coins and few dies, and these values were therefore excluded from the analysis.
The implementation of this tool demonstrates how statistics can advance the study of Iberian coin production by providing results -even if only approximate- that would often be difficult to obtain using traditional counting methods. It is hoped that future numismatic research will, over time, validate the proposed estimates.
Regression model