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In [[statistics]], '''truncation''' results in values that are limited above or below, resulting in a '''truncated sample'''.<ref>[[Yadolah Dodge|Dodge, Y.]] (2003) ''The Oxford Dictionary of Statistical Terms''. OUP. ISBN 0-19-920613-9</ref> Truncation is similar to but distinct from the concept of [[Censoring (statistics)|statistical censoring]]. A truncated sample can be thought of as being equivalent to an underlying sample with all values outside the bounds entirely omitted, with not even a count of those omitted being kept. If the sample had been censored, a record would be of those that were censored, consisting of a note of whether the lower or upper bound had been passed and the value of the bound.
This is a preview for the new '''MathML rendering mode''' (with SVG fallback), which is availble in production for registered users.


==Applications==
If you would like use the '''MathML''' rendering mode, you need a wikipedia user account that can be registered here [[https://en.wikipedia.org/wiki/Special:UserLogin/signup]]
* Only registered users will be able to execute this rendering mode.
* Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.


Usually the values that [[insurance adjuster]]s receive are either left-truncated, right-censored or both.  For example, if policyholders are subject to a policy limit, u, then any loss amounts that are actually above u are reported to the insurance company as being exactly u because u is the amount the [[insurance company|insurance companies]] pay.  The insurance company knows that the actual loss is greater than ''u'' but they don't know what it is.  On the other hand, left truncation occurs when policyholders are subject to a deductible.  If policyholders are subject to a deductible d, any loss amount that is less than d will not even be reported to the insurance company.  If there is a claim on a policy limit of u and a deductible of d, any loss amount that is greater than u will be reported to the insurance company as a loss of u-d because that is the amount the insurance company has to pay.  Therefore insurance loss data is left-truncated because the insurance company doesn't know if there are values below the deductible d because policyholders won't make a claim.  The insurance loss is also right censored if the loss is greater than u because u is the most the insurance company will pay, so it only knows that your claim is greater than u, not what the claim amount is exactly.
Registered users will be able to choose between the following three rendering modes:


==Probability distributions==
'''MathML'''
{{Main|Truncated distribution}}
:<math forcemathmode="mathml">E=mc^2</math>


Truncation can be applied to any [[probability distribution]] and will lead to a new distribution, not usually one within the same family. Thus, if a random variable ''X'' has ''F''(''x'') as its distribution function, the new random variable ''Y'' defined as having the distribution of ''X'' truncated to the semi-open interval (a,b] has the distribution function
<!--'''PNG''' (currently default in production)
:<math forcemathmode="png">E=mc^2</math>


:<math>F_Y(y)=\frac{F(y)-F(a)}{F(b)-F(a)} \,</math>
'''source'''
:<math forcemathmode="source">E=mc^2</math> -->


for ''y'' in the interval (''a'', ''b''], and 0 or 1 otherwise. If truncation were to the closed interval [a,b], the distribution function would be
<span style="color: red">Follow this [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering link] to change your Math rendering settings.</span> You can also add a [https://en.wikipedia.org/wiki/Special:Preferences#mw-prefsection-rendering-skin Custom CSS] to force the MathML/SVG rendering or select different font families. See [https://www.mediawiki.org/wiki/Extension:Math#CSS_for_the_MathML_with_SVG_fallback_mode these examples].


:<math>F_Y(y)=\frac{F(y)-F(a-)}{F(b)-F(a-)} \,</math>
==Demos==


for ''y'' in the interval [''a'', ''b''], and 0 or 1 otherwise.
Here are some [https://commons.wikimedia.org/w/index.php?title=Special:ListFiles/Frederic.wang demos]:


==Data analysis==


The analysis of data where observations are treated as being from truncated versions of standard distributions can be undertaken using a [[maximum likelihood]], where the likelihood would be derived from the distribution or density of the truncated distribution. This involves taking account of the factor <math>{F(b)-F(a)}</math> in the modified density function which will depend on the parameters of the original distribution.  
* accessibility:
** Safari + VoiceOver: [https://commons.wikimedia.org/wiki/File:VoiceOver-Mac-Safari.ogv video only], [[File:Voiceover-mathml-example-1.wav|thumb|Voiceover-mathml-example-1]], [[File:Voiceover-mathml-example-2.wav|thumb|Voiceover-mathml-example-2]], [[File:Voiceover-mathml-example-3.wav|thumb|Voiceover-mathml-example-3]], [[File:Voiceover-mathml-example-4.wav|thumb|Voiceover-mathml-example-4]], [[File:Voiceover-mathml-example-5.wav|thumb|Voiceover-mathml-example-5]], [[File:Voiceover-mathml-example-6.wav|thumb|Voiceover-mathml-example-6]], [[File:Voiceover-mathml-example-7.wav|thumb|Voiceover-mathml-example-7]]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Audio-Windows7-InternetExplorer.ogg Internet Explorer + MathPlayer (audio)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-SynchronizedHighlighting-WIndows7-InternetExplorer.png Internet Explorer + MathPlayer (synchronized highlighting)]
** [https://commons.wikimedia.org/wiki/File:MathPlayer-Braille-Windows7-InternetExplorer.png Internet Explorer + MathPlayer (braille)]
** NVDA+MathPlayer: [[File:Nvda-mathml-example-1.wav|thumb|Nvda-mathml-example-1]], [[File:Nvda-mathml-example-2.wav|thumb|Nvda-mathml-example-2]], [[File:Nvda-mathml-example-3.wav|thumb|Nvda-mathml-example-3]], [[File:Nvda-mathml-example-4.wav|thumb|Nvda-mathml-example-4]], [[File:Nvda-mathml-example-5.wav|thumb|Nvda-mathml-example-5]], [[File:Nvda-mathml-example-6.wav|thumb|Nvda-mathml-example-6]], [[File:Nvda-mathml-example-7.wav|thumb|Nvda-mathml-example-7]].
** Orca: There is ongoing work, but no support at all at the moment [[File:Orca-mathml-example-1.wav|thumb|Orca-mathml-example-1]], [[File:Orca-mathml-example-2.wav|thumb|Orca-mathml-example-2]], [[File:Orca-mathml-example-3.wav|thumb|Orca-mathml-example-3]], [[File:Orca-mathml-example-4.wav|thumb|Orca-mathml-example-4]], [[File:Orca-mathml-example-5.wav|thumb|Orca-mathml-example-5]], [[File:Orca-mathml-example-6.wav|thumb|Orca-mathml-example-6]], [[File:Orca-mathml-example-7.wav|thumb|Orca-mathml-example-7]].
** From our testing, ChromeVox and JAWS are not able to read the formulas generated by the MathML mode.


In practice, if the fraction truncated is very small the effect of truncation might be ignored when analysing data. For example, it is common to use a [[normal distribution]] to model data whose values can only be positive but for which the typical range of values is well away from zero: in such cases a truncated or censored version of the normal distribution may formally be preferable (although there would be other alternatives also), but there would be very little change in results from the more complicated analysis. However, software is readily available for maximum likelihood estimation of even moderately complicated models, such as [[regression analysis|regression models]], for truncated data.<ref>Wolynetz, M.S. (1979) ''Maximum Likelihood estimation in a Linear model from Confined and Censored Normal Data''. J.Roy.Statist.Soc (Series C), 28(2), 195&ndash;206</ref>
==Test pages ==


==See also==
To test the '''MathML''', '''PNG''', and '''source''' rendering modes, please go to one of the following test pages:
*[[Censoring (statistics)]]
*[[Displaystyle]]
*[[Trimmed estimator]]
*[[MathAxisAlignment]]
*[[Truncated (polyhedron)]]
*[[Styling]]
*[[Truncated mean]]
*[[Linebreaking]]
*[[Truncated dependent variable]]
*[[Unique Ids]]
*[[Help:Formula]]


==References==
*[[Inputtypes|Inputtypes (private Wikis only)]]
<references/>
*[[Url2Image|Url2Image (private Wikis only)]]
 
==Bug reporting==
[[Category:Statistical data types]]
If you find any bugs, please report them at [https://bugzilla.wikimedia.org/enter_bug.cgi?product=MediaWiki%20extensions&component=Math&version=master&short_desc=Math-preview%20rendering%20problem Bugzilla], or write an email to math_bugs (at) ckurs (dot) de .
[[Category:Theory of probability distributions]]

Latest revision as of 22:52, 15 September 2019

This is a preview for the new MathML rendering mode (with SVG fallback), which is availble in production for registered users.

If you would like use the MathML rendering mode, you need a wikipedia user account that can be registered here [[1]]

  • Only registered users will be able to execute this rendering mode.
  • Note: you need not enter a email address (nor any other private information). Please do not use a password that you use elsewhere.

Registered users will be able to choose between the following three rendering modes:

MathML

E=mc2


Follow this link to change your Math rendering settings. You can also add a Custom CSS to force the MathML/SVG rendering or select different font families. See these examples.

Demos

Here are some demos:


Test pages

To test the MathML, PNG, and source rendering modes, please go to one of the following test pages:

Bug reporting

If you find any bugs, please report them at Bugzilla, or write an email to math_bugs (at) ckurs (dot) de .

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