Question On Scarcity

The PCGS coin facts site contains survival estimates for U.S. coins. I don't know about Canadian. Just go to the site, find the entry for your date, mint mark and coin type. Under the Rarity tab you will find survival estimates.
I have always been skeptical about relying too much on the survival estimates, particularly for circulated specimens. For example, I have an 1839-O Liberty Seated dime. It is a common issue in circulated condition. Mine is in G-4 condition. I paid $1 for it 50 years ago as a young collector. PCGS estimates that only 600 of this issue survive in all conditions. But the coin in G-4 lists for only $25. A coin as rare as 600 survivors should be priced at least 100 times as much as that, and I never should have been able to get my hands on one. I don't think the circulated coin estimate bears any relation to reality.
I feel much less skeptical about the mint state estimates. People just don't spend the night to grade common low grade coins. So PCGS cannot rely on submission data to estimate how many are left. But the much more valuable mint state coins are more likely to have been submitted than common date low grade specimens. So they can provide some sort of data point for extrapolation. As another example, I have a mint state ms64 graded Liberty Seated dime. PCGS estimates that only 40 survive in mint state. Other sources confirm that the coin is quite rare in mint state, so I am inclined to believe the PCGS mint state survival estimate.
PCGS does not explain its methodology for arriving at its estimates. It just says they are made by a smart, knowledgeable panel of respected professional numismatists. However, I can think of no reason why PCGS would want to publish inaccurate numbers, so I have to assume it is trying its best to be accurate.
I don't think there can be a formula for extrapolating survival from mintage numbers. There are too many variables. But don't rely too much on mintage figures. Depending on the coin, and more so for older coins, there may be little relationship between original mintage figures and present day survival.
So I look at and consider the survival estimates as one factor in evaluating a coin, but I don't treat them as gospel truth.

On the first page select the link for the appropriate series. If more than one type appears in a series, a page will pop up for you to choose the type. Either way, you will get a page to select data and mint mark. Once you select that, you will get an 3-4 entire pages of information about your coin. At the very bottom of each page are a series of tabs for price, population, rarity, and maybe something else. Select Rarity and you will get the survival estimates. I wish I could send you the link with my IPad. The site is called PCGS coin guide. It contains a wealth of information, and I consult it before every purchase. I understand NCG has the same type of site, but I haven't become familiar with it.
Happy hunting!

I think estimating survival rates is a shot in the dark. To get an idea of relative scarcity, you may want to check how many are listed on ebay and how many have sold over time. You could also ask dealers how many they have come across over the years.

It's virtually impossible to create a generic formula that could be applied to any coin series, anywhere in the world. All sorts of factors come into play, some of which are really hard to mathematically quantify:
- Official withdrawal rates. Some countries have always had active withdrawal policies, other countries (eg. America) have had a much more laissez-faire attitude. Some countries keep meticulous records of coins redeemed and destroyed, others don't.
- Amount of money in circulation. A country with very little coin on hand, like colonial Canada and Australia, is going to see coins circulate for far longer than would normally be expected.
- Cultural norms. Would it be considered "normal" or "unusual" in that country for people to, say, bury a stash of coins in their yard? Was coin collecting historically popular there at the time, or not?
- Amount of foreign trade - are foreigners likely to have exported many of the coins? If so, are those coins likely to have been kept intact, or destroyed?

Even within Canada, different coinage series will have different survival rates. For example, I'd reckon that Newfoundland silver coins from the 1800s are more likely to have survived intact than the silver coins of New Brunswick, because they were in circulation for much longer, and therefore more likely to have been lost, hoarded or souvenired (and therefore been spared from recall and melting when the province joined Canada).