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Cumulant — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Cumulant
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-31T08:53:22.594Z
SHA-256 of the archived text: b1be22aa6fd0549b050c0d83f4a589c5de6ce45b0102bc508b3db97240ebf53a
Stable URL of this page: https://metraipolis.com/documento/dc_2040c74587df

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Cumulant — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Cumulant (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_2040c74587df (Metraipolis archive dc_2040c74587df, sha256 b1be22aa6fd0549b050c0d83f4a589c5de6ce45b0102bc508b3db97240ebf53a)

BibTeX

@misc{dc2040c74587df,
  title = {Cumulant — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Cumulant},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_2040c74587df; sha256 b1be22aa6fd0549b050c0d83f4a589c5de6ce45b0102bc508b3db97240ebf53a},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Cumulant. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa. The first cumulant is the mean, the second cumulant is the variance, and the third cumulant is the same as the third central moment. But fourth and higher-order cumulants are not equal to central moments. In some cases theoretical treatments of problems in terms of cumulants are simpler than those using moments. In particular, when two or more random variables are statistically independent, the nth-order cumulant of their sum is equal to the sum of their nth-order cumulants. Also, the third and higher-order cumulants of a normal distribution are zero, and it is the only distribution with this property. Just as for moments, where joint moments are used for collections of random variables, it is possible to define joint cumulants.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «probability theory»).
Fonte: Wikipedia in inglese, voce «Cumulant» — https://en.wikipedia.org/wiki/Cumulant
Wikidata Q746007: «set of quantities that provide an alternative to the moments of the distribution in probability theorie» (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q746007
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Cumulant?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1378013955, consultata il 2026-10-31T08:42:15.210Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: 5b6f1abc240e1b8abb9de48c520aeed1dc4f2c64e11675f2ee311b8217810ba9