https://www.liveauctioneers.com/item/31983903_universal-tri-compax-full-calendar-ref-22258-around

I have 6 examples of reference 22258 and 59 between 946.791 and 997 in my database so I assume a batch of somewhere between 250 and 500 pieces.

 

If you assume that there was one watch of the same model for every serial in the given range, then I think you can treat this like a modified "German Tank Problem" with an unknown starting serial, and this says your estimate for the total should be:

(max_observed - min_observed) * (1 + (2 / (num_observed - 1))) -1

i.e.


In the case above this would yield an estimate of 288 total.

(I'm not quite sure why you can't model it as estimating the bounds of a discrete uniform probability distribution from which you have selected at random, but doing so seems to give slightly different results. )

Edit: missed some parentheses originally...

 

Indeed. This is an early case as evidenced by the protruding corrector buttons. I find in interesting that the moon face isn’t shown.

 

Interesting. I am aware of this approach but it goes a bit above my IQ

I only recorded the case numbers if the movement number was also known. With some (read: perhaps a lot of) digging more serials may be found.

 

The German tank problem is one of these very intruiging WW2 things

 

Another 946.xxx: https://watchcharts.com/listing/639453/universal-geneve-tri-compax-vintage-watch-22258-circa-1943

 

Ok .. play time..is “num observed” = “Max observed - Min Observed” ? Thanks

 

Using @Mark020's numbers:

max_observed = 946,997
min_observed = 946,791
num_observed = 6

The proof in the PDF is a little bit beyond my abilities too, btw; I only play a mathematician on the internet.

 

With the one I posted above it should be 7.

 

In that case you get 274:

https://www.wolframalpha.com/input/?i=(997 - 791) * (1 + (2 / (7 - 1))) -1

The bound gets tighter with additional observations in the same range.

 

I think 22258/9 were made in multiple batches. I have more records - again only: if I have both serial and movement number - than the 6 I mentioned.

However the first batch is all in the range I posted above. So:
Batch 1 946k
Batch 2 1.043m (around)
Batch 3 1.066/1.067m
Batch 4 1.156/1.157m

Total records: 12 of which 9 22258 and 3 22259. The one in Sala is also 946.xxx but unfortunately Sala rarely shows movement pics.

My database started as a fun project but is now a - kind of - addiction. Now over 700 records of serial and movement from app. 700k to 1.9m serials. I will write something about it when I know what I discovered

 

I see. The 274 estimate should be pretty reliable for Batch 1 then, and you could use the same method to estimate the other batches individually.

 

Batch 4 also points to 250, batch 3 to 500. I wont be surpised if these references were made in batches of 250/500.

Another interesting reference - because high number of samples - is 32407 which was typically used for Uweco and Berthoud (13 samples)
Batch 1: 799k (4 samples). Tank number: 614. However: the movement numbers are much closer: within 150. TN based on movements: 226
Batch 2: 834/835k (4 samples). TN: 407. Based on movements: TN 436
Batch 3: 842/842k (5 samples). TN: 1.429. Based on movements: TN 8.099

I'd say that batch 1 and 2 were both 500 pieces and batch 3 1.500. Total production 2.500 pieces.

Yet another: 22209 (total 11 samples) gives the following challenge.
Batch 1: 873k (2 samples). TN: 19. Based on movements: TN 236
Batch 2: 875k (2 samples). TN: 137. Based on movements: TN 239

Or:
Batch 1: 873/875k (4 samples). TN: 3.101. Based on movements: TN 1.822

So: some work to do here

 

Just for the fun of it: ref 31250 (the famous Wilhelmina which is no Wilhelmina). 15 examples.

TN on serials (878-892k): 15.774
TN on movements: 12.316

Another one: 31.230 (11 examples)
TN on serials (1.029-1.032m): 3.866
TN on movements: 16.716

Interesting results

 

Those are fairly big ranges. Do you expect that every consecutive serial from, say, 878-892k was the same model? Does your database not have any other models with a serial in that range?

 

Nope. Just these

 

The PDF you linked is essentially doing this. However, the statistics you are using are the max and min of a sample of size N taken from a discrete uniform distribution. The statistics themselves do not have a discrete uniform distribution. The estimator in the classic GTP is a moment estimator, because the maximum likelihood estimator for the number of tanks is not very useful (it is simply the max observed serial #).

We can continue this discussion over private message if you like. I am familiar with the GTP, but I have not worked through the details of the mondified GTP that I presume are in the appendix. It might be fun to go through it.

 

This is deep. I despised stats class. I’m here for the watch pr0n!

 

Well: pr0n wise I missed out on this one https://www.ebay.nl/itm/184697916963?ul_noapp=truePurchases made through these links may earn this site a commission from the eBay Partner Network
Description: #52203, #1069320. The 17 jewel movement is also signed Universal Geneve & Swiss. It is #235965.
Somebody did a nice deal here I think