normal distribution

English

Four normal distributions

Noun

normal distribution (plural normal distributions)

1. (statistics) Any of a family of continuous probability distributions such that the probability density function is the Gaussian function

   $\varphi _{\mu ,\sigma ^{2}}(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}={\frac {1}{\sigma }}\varphi \left({\frac {x-\mu }{\sigma }}\right),\quad x\in \mathbb {R}$.

   • 2008, James L. Johnson, Probability and Statistics for Computer Science, Wiley, page 437:

     It begins with the normal distribution, which is the limiting form of the sample sum over an arbitrary population.

   • 2012, Larry Pace, Beginning R: An Introduction to Statistical Programming, Apress, page 103:

     The normal distribution is the backbone of traditional statistics. We learn very early in our statistics training that the distribution of sample means, regardless of the shape of the parent distribution, approaches a normal distribution as the sample size increases.

   • 2014, Mohammad Ahsanullah, B.M. Golam Kibria, Mohammad Shakil, Normal and Student's t Distributions and Their Applications‎^[1], Springer (Atlantis Press), page 7:

     The development of the general theories of the normal distributions began with the work of de Moivre (1733, 1738) in his studies of approximations to certain binomial distributions for large positive integer n > 0.

   Synonyms: (informal) bell curve, Gaussian distribution

Usage notes

The probability density function is often represented by the Greek letter $\phi$ or $\varphi$.

Derived terms

• bivariate normal distribution
• log normal distribution
• skew normal distribution
• standard normal distribution

 

Translations

probability distribution

• Azerbaijani: normal paylanma
• Chinese:

  Hokkien: 常態分佈／常态分布 (siông-thài hun-pò͘)

  Mandarin: 正態分佈／正态分布 (zhèngtài fēnbù) (mainland China), 常態分佈／常态分布 (zh) (chángtài fēnbù) (Taiwan)

• Czech: normální rozdělení n
• Danish: normalfordeling
• Dutch: normaalverdeling (nl), normale verdeling (nl), gaussverdeling
• Estonian: normaaljaotus
• Finnish: normaalijakauma (fi)
• French: loi normale f
• Georgian: ნორმალური განაწილება (normaluri ganac̣ileba)
• German: Normalverteilung (de) f, Gauß-Verteilung f
• Hungarian: normális eloszlás (hu), Gauss-eloszlás (hu)
• Icelandic: Gauss-dreifing f, normaldreifing f
• Indonesian: distribusi normal
• Italian: distribuzione normale f
• Kazakh: қалыпты дисперсия (qalypty dispersiä)
• Latin: distributio normalis f
• Lithuanian: normalusis skirstinys
• Malay: taburan normal
• Marathi: सामान्य वितरण (sāmānya vitraṇ)
• Norwegian: normalfordeling m
• Persian: توزیع نرمال
• Polish: rozkład normalny m
• Portuguese: distribuição normal f, distribuição gaussiana f
• Russian: нормальное распределение n (normalʹnoje raspredelenije)
• Slovak: normálne rozdelenie n
• Spanish: distribución normal f
• Swedish: normalfördelning (sv) c
• Tagalog: daniwing pamamahagi
• Thai: การแจกแจงปรกติ
• Ukrainian: норма́льний розпо́діл m (normálʹnyj rozpódil)
• Vietnamese: phân phối chuẩn
• Welsh: dosraniad normal

See also

• central limit theorem
• standard normal deviate