Tango tree - Revision history

en>Erel Segal: /* Interleave Bound */ - add link to main page

2015-01-04T19:18:08Z

Interleave Bound: - add link to main page

← Older revision		Revision as of 21:18, 4 January 2015
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	~~In [[statistics]] the '''trimean (TM)''', or '''Tukey's trimean''',~~ is ~~a measure of a [[probability distribution]]'s [[average\|location]] defined as a [[weighted average]] of~~ the ~~distribution's [[median]] and its two [[quartiles]]:~~		The author is recognized by the title of Numbers Lint. Doing ceramics is what my family members and I appreciate. Managing individuals is his profession. South Dakota is exactly where I've always been living.<br><br>Also visit my site [http://www.streaming.iwarrior.net/blog/396549 std testing at home]

	~~: <math>TM= \frac{Q_1 + 2Q_2 + Q_3}{4}</math>~~

	~~This is equivalent to the average of the [[median]] and the [[midhinge]]:~~

	~~: <math>TM= \frac{1}{2}\left(Q_2 + \frac{Q_1 + Q_3}{2}\right)</math>~~

	The foundations of the trimean were part of [[Arthur Bowley]]'s teachings, and later popularized by statistician [[John Tukey]] in his 1977 book<ref>{{cite book \|last=Tukey \|first=John Wilder \|authorlink= \|coauthors= \|editor= \|others= \|title=Exploratory Data Analysis \|origdate= \|origyear= \|origmonth= \|url= \|format= \|accessdate= \|edition= \|date= \|year=1977 \|month= \|publisher=Addison-Wesley \|location= \|language= \|isbn= 0-201-07616-0 \|doi = \|pages= \|chapter= \|chapterurl= \|quote = }}
	~~</ref> which has given its name to a set~~ of ~~techniques called [[Exploratory data analysis]]~~.

	~~Like the median~~ and ~~the midhinge, but unlike the [[sample mean]], it~~ is ~~a [[statistically resistant]] [[L-estimator]] with a [[Robust statistics#Breakdown point\|breakdown point]] of 25%~~. ~~This beneficial property has been described as follows:~~
	~~{{quote\|An advantage of the trimean as a measure of the center (of a distribution)~~ is ~~that it combines the [[median]]~~'~~s emphasis on center values with the [[midhinge]]'s attention to the extremes~~.~~\|Herbert F. Weisberg\|''Central Tendency and Variability''~~<~~ref~~>Weisberg, H. F. (1992). ''Central Tendency and Variability''. Sage University. ISBN 0-8039-4007-6 ([http://books.google.com/books?id=tPw6b1VXfkoC&pg=PA39&ots=XMd1BObzZr&dq=trimean&sig=WMtwB-23lw44mmnnrrvz4lPHFKQ#PPA39,M1 p. 39])<~~/ref~~>}}

	~~==Efficiency==~~
	Despite its simplicity, the trimean is a remarkably [[Efficiency (statistics)\|efficient]] estimator of population mean. More precisely, for a large data set (over 100 points) from a symmetric population, the average of the 20th, 50th, and 80th percentile is the most efficient 3 point L-estimator, with 88% efficiency.{{sfn\|Evans\|1955\|loc=Appendix G: Inefficient statistics, pp. [http://~~archive~~.org/stream/atomicnucleus032805mbp#page/n925/mode/2up 902–904]}} For context, the best 1 point estimate by L-estimators is the median, with an efficiency of 64% or better (for all ''n''), while using 2 points (for a large data set of over 100 points from a symmetric population), the most efficient estimate is the 29% [[midsummary]] (mean of 29th and 71st percentiles), which has an efficiency of about 81%. Using quartiles, these optimal estimators can be approximated by the midhinge and the trimean. ~~Using further points yield higher efficiency, though it is notable that only 3 points are needed for very high efficiency~~.

	~~==See also==~~
	*[[Truncated mean]]
	*[[Interquartile mean]]

	~~==References==~~
	~~{{reflist}}~~
	~~{{refbegin}}~~
	*{{cite isbn\|0898744148}}
	~~{{refend}}~~

	~~==External links==~~
	*[http://~~mathworld.wolfram.com/Trimean.html Trimean]~~ at ~~[[MathWorld]]~~

	~~[[Category:Summary statistics]]~~
	~~[[Category:Means]]~~
	~~[[Category:Robust statistics]]~~
	~~[[Category:Exploratory data analysis]~~]

en>FrescoBot: Bot: standard sections headers and minor changes

2013-02-25T12:22:05Z

Bot: standard sections headers and minor changes

← Older revision		Revision as of 14:22, 25 February 2013
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	~~Myrtle Benny~~ is ~~how I~~'~~m known~~ as and ~~I really feel comfortable when individuals use~~ the ~~complete~~ title. ~~California~~ is ~~our beginning location~~. ~~One~~ of the ~~extremely very best issues in~~ the ~~globe for me~~ is ~~to do aerobics and now I~~'~~m trying~~ to ~~earn money with it~~. ~~Bookkeeping is my occupation~~.<br>~~<br>my blog~~ [http://~~www~~.~~alhuloul~~.com/?p=~~235037 std home test~~]		In [[statistics]] the '''trimean (TM)''', or '''Tukey's trimean''', is a measure of a [[probability distribution]]'s [[average\|location]] defined as a [[weighted average]] of the distribution's [[median]] and its two [[quartiles]]:

			: <math>TM= \frac{Q_1 + 2Q_2 + Q_3}{4}</math>

			This is equivalent to the average of the [[median]] and the [[midhinge]]:

			: <math>TM= \frac{1}{2}\left(Q_2 + \frac{Q_1 + Q_3}{2}\right)</math>

			The foundations of the trimean were part of [[Arthur Bowley]]'s teachings, and later popularized by statistician [[John Tukey]] in his 1977 book<ref>{{cite book \|last=Tukey \|first=John Wilder \|authorlink= \|coauthors= \|editor= \|others= \|title=Exploratory Data Analysis \|origdate= \|origyear= \|origmonth= \|url= \|format= \|accessdate= \|edition= \|date= \|year=1977 \|month= \|publisher=Addison-Wesley \|location= \|language= \|isbn= 0-201-07616-0 \|doi = \|pages= \|chapter= \|chapterurl= \|quote = }}
			</ref> which has given its name to a set of techniques called [[Exploratory data analysis]].

			Like the median and the midhinge, but unlike the [[sample mean]], it is a [[statistically resistant]] [[L-estimator]] with a [[Robust statistics#Breakdown point\|breakdown point]] of 25%. This beneficial property has been described as follows:
			{{quote\|An advantage of the trimean as a measure of the center (of a distribution) is that it combines the [[median]]'s emphasis on center values with the [[midhinge]]'s attention to the extremes.\|Herbert F. Weisberg\|''Central Tendency and Variability''<ref>Weisberg, H. F. (1992). ''Central Tendency and Variability''. Sage University. ISBN 0-8039-4007-6 ([http://books.google.com/books?id=tPw6b1VXfkoC&pg=PA39&ots=XMd1BObzZr&dq=trimean&sig=WMtwB-23lw44mmnnrrvz4lPHFKQ#PPA39,M1 p. 39])</ref>}}

			==Efficiency==
			Despite its simplicity, the trimean is a remarkably [[Efficiency (statistics)\|efficient]] estimator of population mean. More precisely, for a large data set (over 100 points) from a symmetric population, the average of the 20th, 50th, and 80th percentile is the most efficient 3 point L-estimator, with 88% efficiency.{{sfn\|Evans\|1955\|loc=Appendix G: Inefficient statistics, pp. [http://archive.org/stream/atomicnucleus032805mbp#page/n925/mode/2up 902–904]}} For context, the best 1 point estimate by L-estimators is the median, with an efficiency of 64% or better (for all ''n''), while using 2 points (for a large data set of over 100 points from a symmetric population), the most efficient estimate is the 29% [[midsummary]] (mean of 29th and 71st percentiles), which has an efficiency of about 81%. Using quartiles, these optimal estimators can be approximated by the midhinge and the trimean. Using further points yield higher efficiency, though it is notable that only 3 points are needed for very high efficiency.

			==See also==
			*[[Truncated mean]]
			*[[Interquartile mean]]

			==References==
			{{reflist}}
			{{refbegin}}
			*{{cite isbn\|0898744148}}
			{{refend}}

			==External links==
			*[http://mathworld.wolfram.com/Trimean.html Trimean] at [[MathWorld]]

			[[Category:Summary statistics]]
			[[Category:Means]]
			[[Category:Robust statistics]]
			[[Category:Exploratory data analysis]]

en>Grafen: /* Tango Join algorithm */clean up using AWB

2012-06-17T23:17:17Z

Tango Join algorithm: clean up using AWB

New page

Myrtle Benny is how I'm known as and I really feel comfortable when individuals use the complete title. California is our beginning location. One of the extremely very best issues in the globe for me is to do aerobics and now I'm trying to earn money with it. Bookkeeping is my occupation.<br><br>my blog [http://www.alhuloul.com/?p=235037 std home test]