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- Stability_postulate abstract "In probability theory, to obtain a nondegenerate limiting distribution of the extreme value distribution, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size.If are independent random variables with common probability density function then the cumulative distribution function of is If there is a limiting distribution of interest, the stability postulate states the limiting distribution is some sequence of transformed "reduced" values, such as , where may depend on n but not on x.To distinguish the limiting cumulative distribution function from the "reduced" greatest value from F(x), we will denote it by G(x). It follows that G(x) must satisfy the functional equation This equation was obtained by Maurice René Fréchet and also by Ronald Fisher.Boris Vladimirovich Gnedenko has shown there are no other distributions satisfying the stability postulate other than the following: Gumbel distribution for the minimum stability postulate If and then where and In other words, Extreme value distribution for the maximum stability postulate If and then where and In other words, Fréchet distribution for the maximum stability postulate If and then where and In other words,".
- Stability_postulate wikiPageID "31283248".
- Stability_postulate wikiPageRevisionID "567292964".
- Stability_postulate hasPhotoCollection Stability_postulate.
- Stability_postulate subject Category:Extreme_value_data.
- Stability_postulate subject Category:Probability_theory.
- Stability_postulate type Abstraction100002137.
- Stability_postulate type Cognition100023271.
- Stability_postulate type Datum105816622.
- Stability_postulate type ExtremeValueData.
- Stability_postulate type Information105816287.
- Stability_postulate type PsychologicalFeature100023100.
- Stability_postulate comment "In probability theory, to obtain a nondegenerate limiting distribution of the extreme value distribution, it is necessary to "reduce" the actual greatest value by applying a linear transformation with coefficients that depend on the sample size.If are independent random variables with common probability density function then the cumulative distribution function of is If there is a limiting distribution of interest, the stability postulate states the limiting distribution is some sequence of transformed "reduced" values, such as , where may depend on n but not on x.To distinguish the limiting cumulative distribution function from the "reduced" greatest value from F(x), we will denote it by G(x). ".
- Stability_postulate label "Stability postulate".
- Stability_postulate sameAs m.0gjb551.
- Stability_postulate sameAs Q7595728.
- Stability_postulate sameAs Q7595728.
- Stability_postulate sameAs Stability_postulate.
- Stability_postulate wasDerivedFrom Stability_postulate?oldid=567292964.
- Stability_postulate isPrimaryTopicOf Stability_postulate.