#5652393 - 05/04/1202:13 PMEstimating the number of dies used
RWBRWB
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Here's a brief example of how to calculate the total number of dies used if you have only incomplete die data. Seems useful for early copper and silver fans.
Example 1. This interesting example was described in Holst (1981). Given the number of dies having produced r coins, r= 1, 2, ... in a hoard, the problem is to estimate the number of dies used in the minting process. We first discuss the reverse side: 204 coins were found in a hoard of ancient coins, 156 dies appeared once, 19 twice, 2 three times, and 1 four times, no die appeared more than four times. For this frequency sequence, as explained by Holst (1981), it is plausible to assume that all the classes are equally likely. He further obtained an estimate 731 of the number of classes and constructed a 95% confidence interval (537, 1 106). The jackknife estimate is the sixth order value 06=854 with a standard error 107.7, which yields an interval (643, 1065) assuming the normality is valid. Esty (1983) obtained a confidence interval for the sample coverage and thus gave an estimate 757 and the interval (559, 1171) under the restrictive equiprobability assumption. The estimate proposed in this work is 0=818. B= 1000 replications were then drawn from the following "pseudo population": 717 cells with probabilities 1/938, 87 cells with probabilities 2/938, 9 cells with probabilities 3/938, and 5 cells with probabilities 4/938. The percentile method gives an interval (522, 1 218). All the results are comparable. Although our interval is wider, we will see, in Example 4, that the coverage probability of it is closer to the nominal level than that of the jackknife interval.
[See “Nonparametric Estimation of the Number of Classes in a Population,” Anne Chao, National Tsing Hua University, 1984, or the formulas.]
(PS: The final range is from 218 to 522 dies were used.)
Edited by RWB (05/04/1203:17 PM)
_________________________
Author of “Renaissance of American Coinage” (NLG Book-of-the-Year 3 years in a row) series and “Guide Book of Peace Dollars,” NLG 2011-Best Software: “Annual Assay Commission, United States Mint, 1800-1943,” and “Silver Dollars Struck under the Pittman Act.” Federal Court-approved numismatic expert. Contributor to the Red Book, Judd Patterns and many other fine numismatic books, discoverer of two gold patterns, and author of numerous coin research articles.
#5652751 - 05/04/1204:48 PMRe: Estimating the number of dies used
[Re: RWB]
WoodenJeffersonWoodenJefferson I have nothing to add or subtract, I am merely here.
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Registered: 12/08/06
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Do you really think this question can be scientifically answered as such with any sort of accuracy...tuns out the final range from 218 to 522 dies used is a pretty impressive range?
I'd much rather take the mints estimated production amounts and estimate coins struck per die...taking into account dies failing early and dies used beyond their actual intended life. It may not be very accurate, but I would feel more comfortable with the results, rather than working solely on frequency evaluations.
#5652952 - 05/04/1205:58 PMRe: Estimating the number of dies used
[Re: WoodenJefferson]
RWBRWB
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Jeff - Did you read the article? If not, then how do you reach your conclusions? (There was no comment about what you call "scientific accuracy" – whatever that is supposed to mean.) Did you “know” you liked steak before you first ate one?
The example refers to a small, skewed hoard of ancient coins. Did you apply the formulas to 1794 cents or half cents?
_________________________
Author of “Renaissance of American Coinage” (NLG Book-of-the-Year 3 years in a row) series and “Guide Book of Peace Dollars,” NLG 2011-Best Software: “Annual Assay Commission, United States Mint, 1800-1943,” and “Silver Dollars Struck under the Pittman Act.” Federal Court-approved numismatic expert. Contributor to the Red Book, Judd Patterns and many other fine numismatic books, discoverer of two gold patterns, and author of numerous coin research articles.
#5653082 - 05/04/1206:36 PMRe: Estimating the number of dies used
[Re: WoodenJefferson]
RWBRWB
FACT if I stop posting, trillions and trillions of transistors would be out of work.
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Me either.....but this might be a way to help predict, or verify something we are not sure of today...or maybe not....trying it is what counts.
The original article in available on the internet - free.
_________________________
Author of “Renaissance of American Coinage” (NLG Book-of-the-Year 3 years in a row) series and “Guide Book of Peace Dollars,” NLG 2011-Best Software: “Annual Assay Commission, United States Mint, 1800-1943,” and “Silver Dollars Struck under the Pittman Act.” Federal Court-approved numismatic expert. Contributor to the Red Book, Judd Patterns and many other fine numismatic books, discoverer of two gold patterns, and author of numerous coin research articles.
#5654279 - 05/05/1208:43 AMRe: Estimating the number of dies used
[Re: RWB]
RWBRWB
FACT if I stop posting, trillions and trillions of transistors would be out of work.
Registered: 01/03/05
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For those who might find this subject interesting, please read the articles by Dr. Warren Esty, Professor of Mathematics, Montana State University. westy@math.montana.edu
_________________________
Author of “Renaissance of American Coinage” (NLG Book-of-the-Year 3 years in a row) series and “Guide Book of Peace Dollars,” NLG 2011-Best Software: “Annual Assay Commission, United States Mint, 1800-1943,” and “Silver Dollars Struck under the Pittman Act.” Federal Court-approved numismatic expert. Contributor to the Red Book, Judd Patterns and many other fine numismatic books, discoverer of two gold patterns, and author of numerous coin research articles.
Hmmm....ok, I will first state that my training is in engineering, not statistics. That being said, statistics is a subject I am somewhat familiar with. The problem with the analysis IMO has to do with the sample size. 204 coins simply cannot give a high confidence number when you are talking about a total population in the millions. That is the reason the result gives such a large deviation. To increase the confidence level, the sample size needs to be larger, or a multiple number of small random samples need to be collected, which in effect increases the sample size.
#5661954 - 05/08/1211:56 AMRe: Estimating the number of dies used
[Re: Crohnos01]
RWBRWB
FACT if I stop posting, trillions and trillions of transistors would be out of work.
Registered: 01/03/05
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Agreed. Warren Esty's approach includes the realities of numismatics. Might be useful in confirming number of dies made/used, etc.
_________________________
Author of “Renaissance of American Coinage” (NLG Book-of-the-Year 3 years in a row) series and “Guide Book of Peace Dollars,” NLG 2011-Best Software: “Annual Assay Commission, United States Mint, 1800-1943,” and “Silver Dollars Struck under the Pittman Act.” Federal Court-approved numismatic expert. Contributor to the Red Book, Judd Patterns and many other fine numismatic books, discoverer of two gold patterns, and author of numerous coin research articles.
