Estimation of the Size of a Coinage: A Survey and Comparison of Methods

Estimators of the size of an ancient coinage and the number of dies used to produce it are compared by evaluating their accuracy when applied to computer-simulated hoards that represent both random and non-random samples from issues with various types of die-outputs. Summary statistics of the results of the computer simulations are presented, and the best estimator is selected by inspection of the summaries of the cases deemed of greatest interest. In the Appendices the formulae are given and the estimators are discussed theoretically. Some are eliminated from further consideration for theoretical reasons, and some because other computer simulations demonstrate that they have undesirable properties. Estimation of the size of a coinage is most accurate when it proceeds from estimation of the coverage, rather than from estimation of the number of dies, because the method has smaller errors at each of the steps. The best coverage estimator is that of Good. Surprisingly, the best estimator of the number of dies is a modification of the same method, and not one of the estimators specifically designed to estimate the number of dies. The Good estimator is valid regardless of the variation in die-output and relatively insensitive to errors induced by nonrandom sampling; it is also of comparable accuracy to the best parametric estimators when the sample is random. A method is given for converting coverage estimators to die-number estimators and vice versa if the variation in die-output is specified. This method, combined with the Good coverage estimator, creates an estimator of the number of dies that can deal with unequal die-outputs with various distributions.