For some years the equations proposed by Warren Esty have been used to estimate the number of dies used to strike a particular issue or coinage. The equations are used to give point estimates of the number of dies and the coverage and also 95% confidence limits on these numbers. However, the equations are based on assumptions, and as reasonable as they are, it is still only a model, and therefore the question has often been asked “do you believe the results?”
The acquisition of an 1865 shilling with the die number 102 (a rarity according to specialist collectors) led to the realisation that a study of the die numbered coinage can be used to test the statistical models. This is simply because we know what the answer is, as the dies are all numbered.
A virtual collection of 184 shillings dated 1865 was gathered and used to systematically test the statistical methods with increasing sample size. This confirms that the equations work quite well. Taking the analysis further, data from specialist collectors (David Morley and Ron Stafford) add a further 764 shillings dated 1865 to the study. With a coverage of 0.98 the number of dies is estimated to be 131 (95% within 126 to 137) which compares extremely well with the 122 different dies that are known from the highest die number of 130.
BNS Research Blog 