Deltahedron: /* References */ expand bibliodata

2014-07-25T18:19:15Z

References: expand bibliodata

← Older revision		Revision as of 20:19, 25 July 2014
Line 1:		Line 1:
	~~The '''Lincoln index'''~~ is ~~a statistical measure used in several fields to [[estimator\|estimate]]~~ the ~~number of cases~~ that ~~have not yet been observed, based on two independent sets~~ of ~~observed cases~~. ~~Described by [[Frederick Charles Lincoln]] in 1930~~, it ~~is also sometimes known as~~ the ~~'''Lincoln-Petersen method''' after [[C~~.~~G. Johannes Petersen]] who~~ was ~~the first to use the related [[mark and recapture]] method~~.~~<ref name="Southwood">Southwood, T.R.E. & Henderson, P. (2000) ''Ecological Methods'', 3rd edn. Blackwell Science, Oxford.</ref>~~		Gold is one of the most beautiful and most precious metals that man has ever discovered. It is the ultimate source of wealth and value. Even during the ancient times, people are aware of its value making it the medium of exchange. Gold was still traded until 30 years ago. The power of Gold surpasses that of the dollar. To prove this, take a look back into history. The value of the dollar has plunged since the collapse of the Bretton Wood agreement. Coincidence you may say? Maybe not.<br><br><br><br>If you are investing in gold/silver to hedge against inflation, collectibles are definitely not the way to go as you'll pay a premium for the metal content in the coin.<br><br>gold coins are easy to sell - Liquidity is an important factor in any investment, and gold coins are easier http://coins.goldgrey.org ([http://coins.goldgrey.org Read Home Page]) to sell than gold bars. There are no delays in the sale process whatsoever. You receive your payment immediately.<br><br>It's called junk, but it's anything but that. This term refers to commonly used dimes or quarters and half dollars that were [http://www.adobe.com/cfusion/search/index.cfm?term=&minted+prior&loc=en_us&siteSection=home minted prior] to 1965 in the United States. Before that time, money contained 90% silver. These silver coins are in good condition, making the term "junk" as misnomer, but they have no numismatic or collectible value except that of the silver it contains. However, since they haven't been minted since 1964, and most of the junk silver has already been melted down, there is speculation that some day junk silver will have its own premium above silver.<br><br>Over the past 10 years, Alan Greenspan, the highly respected former chairman of the U.S. Federal Reserve has seen gold as an investment as a wise choice that he has recommended to others as well. He has even gone so far as to say that while fiat money is going to be worthless someday, gold will still be accepted.<br><br>With almost every stock dipping in its value, and further expected market crises, there is no better time than now to invest in gold and be a part of the buyers gold market. Past statistics and market today state the final word- Invest today, become a gold king tomorrow.<br><br>If you want immediate cash, selling to refiners is the best choice but you will only get paid for the silver content of your item. Refiners will not care about its fine craftsmanship, purity, rarity or its historical value. So if you are not in a financial bind, it is better to look for a buyer who will pay you for the overall value of the piece. Refiners will just separate the silver in the form of a nugget and sell it to silversmiths to be made into new jewelleries.<br><br>If you are still having a hard time coming up with the clues, try doing the scavenger hunt backwards. Start with the last item on the list and work your way down. You can also fine tune your scavenger hunt by playing the game yourself. The trial and error method is a good way to work out the bugs and kinks that might be there. All items on the list do not have to be found. Younger children may not want to continue with the hunt or have a hard time finishing the game, so in case of a tie, come up with a back-up clue or item that can easily be found.<br><br>Certainly coin collecting is not only a pastime but a gifted investment as well. As stated by the World Gold council, they see positive returns in this year at least. In these trying times where the economy is volatile in the US and certain European countries coupled by the sovereign adversity and security risks the gold industry is seeing a bright future and this includes the American eagle gold coin. So what are you waiting for? Start investing now!

	~~==Applications==~~
	~~Consider two observers who separately count the different species~~ of plants or animals in a given area. If they each come back having found 100 species but only 5 particular species are found by ''both'' observers, then each observer clearly missed at least 95 species (that ~~is,~~ the ~~95 that only the other observer found)~~. ~~Thus~~, ~~we know that both observers miss~~ a ~~lot~~. On the ~~other hand, if 99 of~~ the ~~100 species each observer found had been found by both, it is fair to expect that they have found a far higher percentage~~ of the ~~total species that are there to find~~.

	~~The same reasoning applies to [[mark and recapture]]~~. If ~~some animals~~ in ~~a given area~~ are ~~caught and marked, and later~~ a ~~second round of captures is done:~~ the ~~number of marked animals found~~ in the ~~second round can be used to generate an estimate of the total population~~.<~~ref~~>~~{{Cite web \|title=Estimating Population Sizes by Mark~~-~~recapture~~ and ~~Removal Sampling Methods \|url=~~http://~~www~~.~~sbs~~.~~utexas.edu~~/~~jcabbott~~/~~courses/bio208web/labs/populations/populations~~.~~htm \|publisher=University of Texas }}</ref>~~

	~~Another example arises~~ in ~~[[computational linguistics]] for estimating~~ the ~~total vocabulary of a language~~. ~~Given two independent samples~~, ~~the overlap between their vocabularies enables a useful estimate of how many more vocabulary items exist~~ but ~~did not happen~~ to ~~show up in either sample~~. ~~A similar example involves estimating the number of typographical errors remaining in a text, from two proofreaders' counts~~.

	==~~Formulation~~==
	~~The Lincoln Index formalizes this phenomenon~~. ~~If E1 and E2~~ are the ~~number~~ of ~~species (or words~~, ~~or other phenomena) observed by two independent methods~~, and ~~S is~~ the ~~number of observations in common~~, ~~then the Lincoln Index~~ is ~~simply~~

	<~~math~~>~~L={E_1 E_2 \over S}~~<~~/math~~>

	If S ~~= 0 (~~that is, if there is no ~~overlap), then~~ the ~~Lincoln Index is undefined~~ and ~~no estimate~~ is ~~justified. This can arise if~~ the ~~observers~~ only ~~find a small percentage~~ of ~~the actual species (perhaps by~~ not ~~looking hard enough~~ or ~~long enough),~~ if ~~the observers are using methods that~~ are not ~~statistically independent (~~for ~~example if one looks only~~ for ~~large creatures and~~ the ~~other only for small), or in other circumstances~~.

	~~==Limitations==~~
	~~The Lincoln Index is merely an estimate. For example,~~ the ~~species~~ in a ~~given area could tend~~ to ~~be either very common or very rare, or tend~~ to be ~~either very hard or very easy to see~~.<~~ref~~>~~{{Cite journal \|author=T~~. ~~Bohlin \|coauthor=B. Sundstrom \|title=Influence of unequal catchability~~ on ~~population estimates using~~ the ~~Lincoln~~ and the ~~removal~~ method ~~applied~~ to ~~electro-fishing \|journal=OIKOS \|number=28 \|year=1977 \|pages=123–129 \|jstor=3543331 }}</ref> Then it would be likely that both observers would find a large share of~~ the ~~common species,~~ and that ~~both observers would miss a large share of~~ the ~~rare ones~~. ~~Such distributions would throw off~~ the ~~consequent estimate. However~~, ~~such distributions are unusual for natural phenomena~~, ~~as suggested by [[Zipf's Law]]).~~

	~~T. J. Gaskell and B. J. George propose an enhancement of the Lincoln Index~~ that ~~claims to reduce bias~~.<~~ref~~>~~Gaskell and George (1972)~~<~~/ref~~>

	~~==Notes==~~
	~~{{reflist}}~~

	~~==References==~~
	* {{Cite journal \|author=T. ~~J. Gaskell \|coauthor=B. J. George \|title=A Bayesian Modification of~~ the ~~Lincoln Index \|journal=Journal of Applied Ecology \|~~year~~=1972\|volume=9\|issue=2\|pages=377–384 \|jstor=2402438}}~~

	~~==Further reading==~~
	* {{cite book\|last=Lincoln\|first=Frederick C.~~\|title=Calculating Waterfowl Abundance on~~ the Basis of Banding Returns\|date=May 1930\|publisher=United States Department of Agriculture\|location=Washington, DC\|url=http://archive.org/details/calculatingwater118linc\|series=Circular\|volume=118\|accessdate=21 May 2013}}
	*Petersen, C. G. J. (1896). "The Yearly Immigration of Young Plaice Into the ~~Limfjord From~~ the ~~German Sea", ''Report of~~ the ~~Danish Biological Station (1895)'', 6, 5–84~~.

	~~[[Category:Ecological techniques]]~~
	~~[[Category:Data analysis]]~~
	~~[[Category:Environmental statistics]]~~

en>AK456: WP:DPL

2012-07-18T08:19:30Z

WP:DPL

New page

The '''Lincoln index''' is a statistical measure used in several fields to [[estimator|estimate]] the number of cases that have not yet been observed, based on two independent sets of observed cases. Described by [[Frederick Charles Lincoln]] in 1930, it is also sometimes known as the '''Lincoln-Petersen method''' after [[C.G. Johannes Petersen]] who was the first to use the related [[mark and recapture]] method.<ref name="Southwood">Southwood, T.R.E. & Henderson, P. (2000) ''Ecological Methods'', 3rd edn. Blackwell Science, Oxford.</ref>

==Applications==
Consider two observers who separately count the different species of plants or animals in a given area. If they each come back having found 100 species but only 5 particular species are found by ''both'' observers, then each observer clearly missed at least 95 species (that is, the 95 that only the other observer found). Thus, we know that both observers miss a lot. On the other hand, if 99 of the 100 species each observer found had been found by both, it is fair to expect that they have found a far higher percentage of the total species that are there to find.

The same reasoning applies to [[mark and recapture]]. If some animals in a given area are caught and marked, and later a second round of captures is done: the number of marked animals found in the second round can be used to generate an estimate of the total population.<ref>{{Cite web |title=Estimating Population Sizes by Mark-recapture and Removal Sampling Methods |url=http://www.sbs.utexas.edu/jcabbott/courses/bio208web/labs/populations/populations.htm |publisher=University of Texas }}</ref>

Another example arises in [[computational linguistics]] for estimating the total vocabulary of a language. Given two independent samples, the overlap between their vocabularies enables a useful estimate of how many more vocabulary items exist but did not happen to show up in either sample. A similar example involves estimating the number of typographical errors remaining in a text, from two proofreaders' counts.

==Formulation==
The Lincoln Index formalizes this phenomenon. If E1 and E2 are the number of species (or words, or other phenomena) observed by two independent methods, and S is the number of observations in common, then the Lincoln Index is simply

<math>L={E_1 E_2 \over S}</math>

If S = 0 (that is, if there is no overlap), then the Lincoln Index is undefined and no estimate is justified. This can arise if the observers only find a small percentage of the actual species (perhaps by not looking hard enough or long enough), if the observers are using methods that are not statistically independent (for example if one looks only for large creatures and the other only for small), or in other circumstances.

==Limitations==
The Lincoln Index is merely an estimate. For example, the species in a given area could tend to be either very common or very rare, or tend to be either very hard or very easy to see.<ref>{{Cite journal |author=T. Bohlin |coauthor=B. Sundstrom |title=Influence of unequal catchability on population estimates using the Lincoln and the removal method applied to electro-fishing |journal=OIKOS |number=28 |year=1977 |pages=123–129 |jstor=3543331 }}</ref> Then it would be likely that both observers would find a large share of the common species, and that both observers would miss a large share of the rare ones. Such distributions would throw off the consequent estimate. However, such distributions are unusual for natural phenomena, as suggested by [[Zipf's Law]]).

T. J. Gaskell and B. J. George propose an enhancement of the Lincoln Index that claims to reduce bias.<ref>Gaskell and George (1972)</ref>

==Notes==
{{reflist}}

==References==
* {{Cite journal |author=T. J. Gaskell |coauthor=B. J. George |title=A Bayesian Modification of the Lincoln Index |journal=Journal of Applied Ecology |year=1972|volume=9|issue=2|pages=377–384 |jstor=2402438}}

==Further reading==
* {{cite book|last=Lincoln|first=Frederick C.|title=Calculating Waterfowl Abundance on the Basis of Banding Returns|date=May 1930|publisher=United States Department of Agriculture|location=Washington, DC|url=http://archive.org/details/calculatingwater118linc|series=Circular|volume=118|accessdate=21 May 2013}}
*Petersen, C. G. J. (1896). "The Yearly Immigration of Young Plaice Into the Limfjord From the German Sea", ''Report of the Danish Biological Station (1895)'', 6, 5–84.

[[Category:Ecological techniques]]
[[Category:Data analysis]]
[[Category:Environmental statistics]]

Interlocking interval topology - Revision history

Deltahedron: /* References */ expand bibliodata

en>AK456: WP:DPL