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In [[probability theory]], '''Cantelli's inequality''', named after [[Francesco Paolo Cantelli]], is a generalization of [[Chebyshev's inequality]] in the case of a single "tail".<ref>''Research and practice in multiple criteria decision making: proceedings of the XIVth International Conference on Multiple Criteria Decision Making (MCDM), Charlottesville, Virginia, USA, June 8–12, 1998'', edited by Y.Y. Haimes and R.E. Steuer, [[Springer Verlag|Springer]], 2000, ISBN 3540672664.</ref><ref>[http://www.cse.buffalo.edu/~hungngo/classes/2011/Spring-694/lectures/l4.pdf "Tail and Concentration Inequalities" by Hung Q. Ngo]</ref><ref>[http://www.econ.upf.edu/~lugosi/anu.pdf "Concentration-of-measure inequalities" by Gábor Lugois]</ref> The inequality states that


: <math>
\Pr(X-\mu\ge\lambda)\quad\begin{cases}
\le \frac{\sigma^2}{\sigma^2 + \lambda^2} & \text{if } \lambda > 0, \\[8pt]
\ge 1 - \frac{\sigma^2}{\sigma^2 + \lambda^2} & \text{if }\lambda < 0.
\end{cases}
</math>


where
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Ltd. All legal rights reserved. For reprint legal rights: Moments Syndication ServiceFind this comment offensive?nChoose your reason beneath and click on the Submit button. This will notify our moderators to consider actionnNamennExplanation for reporting:nFoul languageSlanderousInciting hatred in opposition to a particular communitySpam/out of contextOthersnnYour Explanation has been Submitted to the admin.nnWhile observing her off to Canada, minor did her neighbours think about that the girl-up coming-doorway in Chandigarh, Guddu, would turn into RJ Aman, and make an identification as a woman aggressively operating to encourage Punjabi heritage amid NRIs settled in Canad<br><br>
 
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:<math>X</math> is a real-valued [[random variable]],
:<math>\Pr</math> is the [[probability measure]],
:<math>\mu</math> is the [[expected value]] of <math>X</math>,
:<math>\sigma^2</math> is the [[variance]] of <math>X</math>.
 
 
 
With the same methods one can prove the following variant:
 
: <math>
\Pr(|X-\mu|\ge\lambda)\le \frac{2\sigma^2}{\sigma^2+\lambda^2}.
</math>
 
 
 
The inequality is due to [[Francesco Paolo Cantelli]]. The Chebyshev inequality implies that in any [[sample (statistics)|data sample]] or [[probability distribution]], "nearly all" values are close to the [[expected value|mean]] in terms of the [[absolute value]] of the difference between the points of the data sample and the weighted average of the data sample. The Cantelli inequality (sometimes called the "Chebyshev–Cantelli inequality" or the "one-sided Chebyshev inequality") gives a way of estimating how the points of the data sample are bigger than or smaller than their weighted average without the two tails of the absolute value estimate. The Chebyshev inequality has [[Chebyshev's inequality#Higher moments|"higher moments versions"]] and [[Chebyshev's inequality#Vector version|"vector versions"]], and so does the Cantelli inequality.
 
==References==
{{reflist}}
 
 
{{probability-stub}}
 
[[Category:Probability theory]]

Revision as of 06:06, 7 February 2014


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Originally, we utilised to talk about our culture and heritage in our social gatherings. My family and pals inspired me to commence some thing on these strains. Considering that I had some expertise in the university times, I opted for a radio present and began as a co-host. For the past close to two years, I have my own show. Now, not just my youngsters, but the youngsters of all Punjabis - like these from Pakistan and some other locations - interact and sing along," she added. nn"Apart from Full Masti and Gup-shup, this programme is my humble endeavor to remain in contact with the sturdy roots that India and Pakistan have supplied, besides celebrating the wings that our new property - Canada has given us. Naal Virse de Jurr ke rahange, for every ethe di vi gal karange ("We shall talk about Canada, but not at the cost of our cheap ugg boots wealthy heritage"), said Aman. nn"Our exhibits encourage each other to be better and do better. We draw inspiration from our scriptures - be it Shabad, Bhajan, Bible http://tinyurl.com/pch83be verses, Quran di aayat, or motivational prices," she insisted. nnAman chats with experts from in the community to learn their secrets and techniques of accomplishment, which in change helps everybody increase their skills and better combine into the mainstream neighborhood. 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Non-logged-in feedback will go through a verification method for safety factors.nnLog in to publish this commentnnYour commentnnCharacters Remaining: 3000nnRefrain from submitting remarks that are obscene, libellous, slanderous or inflammatory, and do not indulge in personalized attacks, identify contacting or inciting hatred against any group. Help us delete responses that do not follow these recommendations by marking them offensive. Let us operate collectively to hold the discussion civil. nnSubmit CommentnPost your commentnnWe inspire you to register/login and move forward.nHowever, if you select to remain non-loggedin, you are required to fill up the sort under and verify your e-mail deal with before we can publish your comment.nThat way, we can confirm that the e-mail deal with doesn't belong to someone else.nRegister/LoginnProceed With out RegistrationnnFull Name nnLocation nnEmail nnFix six + =2nnnnProceed nnPost your commentnnWe inspire you to sign-up/login and move forward.nHowever, if you decide on to continue to be non-loggedin, you are essential to fill up the kind underneath and verify your e-mail address ahead of we can publish your remark.nThat way, we can verify that the electronic mail tackle does not belong to a person else.nRegister/LoginnProceed With out RegistrationnnFull Title nnLocation nnEmail nnFix six + =twonnnnProceed nnnnnThanks! nnWe have despatched you a verification e mail.nTo confirm, just follow the hyperlink in the message nnResend verification mailEmail despatchednnnSort by:Newest|Oldest|Recommended|Most Mentioned|Agree|DisagreeConnect with usFEATURED Today IN US & Canada NewsIndian activist poised to be initial at any time elected socialist in USnIndian-American surgeon gets optimum US immigrant awardnHave world's best task, says US lawful star Preet BhararanPromoting Punjabi heritage in CanadanChhath Puja celebrated in USnmoreYOUR FRIENDS' ACTIVITY1of1FEATURED Today IN NRIIndian jailed in Moscow for $18 million fraudn3 of Indian-origin among Africa's fifty richest: ForbesnIndian origin sisters sentenced for theftnProtests in Uk in help of Indian demise row convict in UAEnIndo-Canadian lady alleges racism in Vancouver barn10 Indians arrested in Uk for immigration offencesn80-year-previous Sikh attacked by lady in British isles diesnRs 1 crore relief for kin of NRI killed in mishapn1 in 10 medical doctors practising in United kingdom is from IndianDo Indians turn out to be far more religious when overseas?nmoreTOP STORIESOnion rates up 278%, tomato 122% in a single yearnAt nine.30am these days, India will appear to a halt as Sachin resumes his innings at 38 in final TestnMeet the thirteen-yr-old lady from Lucknow who is pursuing MSc in microbiologynIndian poised to be very first elected socialist in USnVolvo hearth: Techie smashed pane with head, saved manynmoreMOST POPULARReadn|nCommentedn|nSharednFrom NRI3 of Indian-origin between Africa's 50 richest: ForbesnIndian activist poised to be very first at any time elected socialist in USnIndian-American surgeon gets greatest US immigrant awardnIndian origin sisters sentenced for theftnmoreAcross Moments of IndiaDoodle 4 Google winner's entry marks Children's DaynInd vs WI: Sachin Tendulkar takes India to 157/two at stumps on Day 1 of 2nd TestnRajiv Gandhi wished Bofors cash to run Congress: Ex-CBI chiefn'With Sachin Paaji, a portion of me will be long gone too'nmoreAllnTOInMy ProfilenSign into earn your BadgesKnow far more about Moments PointsTHE Instances OF INDIAnPowered by INDIATIMESnAbout usnnPromote with usnnTerms of Use and Grievance Redressal CoveragennPrivacy plannnFeedbacknnRSSnnNewsletternnTOI MobilennePapernnSitemapnnArchivesnOther Moments Team news sitesnTimes Crest | The Economic Timesn&#x907&#x915&#x928&#x949&#x92e&#x93f&#x915 &#x91f&#x93e&#x907&#x92e&#x94d&#x938 | &#xa88&#xa95&#xacb&#xaa8&#xacb&#xaae&#xabf&#xa95 &#xa9f&#xabe&#xa88&#xaae&#xacd&#xab8nPune Mirror | Bangalore MirrornAhmedabad Mirror | ItsMyAscentnEducation Occasions | Brand CapitalnMumbai Mirror | Times NownIndiatimes | &#x928&#x935&#x92d&#x93e&#x930&#x924 &#x91f&#x93e&#x907&#x92e&#x94d&#x938n&#x92e&#x939&#x93e&#x930&#x93e&#x937&#x94d&#x91f&#x94d&#x930 &#x91f&#x93e&#x907&#x92e&#x94d&#x938 | &#xcb5&#xcbf&#xc9c&#xcaf &#xc95&#xcb0&#xccd&#xca8&#xcbe&#xc9f&#xc95nGo GreenLiving and entertainmentnTimescity | iDiva | Bollywood | ZoomnHealthmeup | Luxpresso | TechnoholiknGuylife | On the internet SongsnnCuriosity Networknitimes | EmailHot on the WebnHotklix | World | PoliticsnBusiness | SportsnEntertainmentnScience & TechnNew CarsServicesnBook print ads | On-line purchasing | Cost-free SMS | Site design | CRM | TendersnMatrimonial | Ringtones | Astrology | Work | Tech Neighborhood | Residence | Acquire carnBikes in India | Offers | Cost-free Classifieds | Send out income to India | Utilised CarsnRestaurants in Delhi | Motion picture Display Timings in Mumbai | Remit to India | Buy MobilesnListen Tracks | Information | Real Estate DevelopersnnTrending TopicsnYahoo | Intercourse | You Tube | Gold Price tag | Twitter | Irctc | Renault Duster | View Videos | Aadhar Card | Facebook | UID CardCopyright � 2013 Bennett, Coleman & Co. Ltd. All legal rights reserved. For reprint legal rights: Moments Syndication ServiceFind this comment offensive?nChoose your reason beneath and click on the Submit button. This will notify our moderators to consider actionnNamennExplanation for reporting:nFoul languageSlanderousInciting hatred in opposition to a particular communitySpam/out of contextOthersnnYour Explanation has been Submitted to the admin.nnWhile observing her off to Canada, minor did her neighbours think about that the girl-up coming-doorway in Chandigarh, Guddu, would turn into RJ Aman, and make an identification as a woman aggressively operating to encourage Punjabi heritage amid NRIs settled in Canad

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