Normální (nebo Gaussovo) rozdělení pravděpodobnosti je jedno z nejdůležitějších rozdělení pravděpodobnosti spojité náhodné veličiny. Slovo „normální“ zde není použito v obvyklém smyslu „obyčejné, běžné“.

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  • In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known.The normal distribution is immensely useful because of the central limit theorem, which states that, under mild conditions, the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution: physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have a distribution very close to the normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.The Gaussian distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as Cauchy's, Student's, and logistic). The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities.A normal distribution isThe parameter μ in this definition is the mean or expectation of the distribution (and also its median and mode). The parameter σ is its standard deviation; its variance is therefore σ 2. A random variable with a Gaussian distribution is said to be normally distributed and is called a normal deviate.If μ = 0 and σ = 1, the distribution is called the standard normal distribution or the unit normal distribution, and a random variable with that distribution is a standard normal deviate.The normal distribution is the only absolutely continuous distribution all of whose cumulants beyond the first two (i.e., other than the mean and variance) are zero. It is also the continuous distribution with the maximum entropy for a given mean and variance.The normal distribution is a subclass of the elliptical distributions. The normal distribution is symmetric about its mean, and is non-zero over the entire real line. As such it may not be a suitable model for variables that are inherently positive or strongly skewed, such as the weight of a person or the price of a share. Such variables may be better described by other distributions, such as the log-normal distribution or the Pareto distribution.The value of the normal distribution is practically zero when the value x lies more than a few standard deviations away from the mean. Therefore, it may not be an appropriate model when one expects a significant fraction of outliers—values that lie many standard deviations away from the mean — and least squares and other statistical inference methods that are optimal for normally distributed variables often become highly unreliable when applied to such data. In those cases, a more heavy-tailed distribution should be assumed and the appropriate robust statistical inference methods applied.The Gaussian distribution belongs to the family of stable distributions which are the attractors of sums of independent, identically distributed distributions whether or not the mean or variance is finite. Except for the Gaussian which is a limiting case, all stable distributions have heavy tails and infinite variance.
  • В теория на вероятностите и статистиката нормалното разпределение или разпределението на Гаус e непрекъснато разпределение на вероятност, което често дава добър опис на пробите, групиращи се около средна стойност. Графиката на функцията на плътност на вероятността е с формата на камбана, с максимум в средната стойност, и е известна като функция на Гаус. Разпределението на Гаус е само едно от многото неща, носещи името на Карл Фридрих Гаус, които той използвал за анализ на астрономически данни, и да определи формулата за неговата функция на плътност на вероятността. Въпреки това Гаус не е бил първият, който е изследвал това разпределение или формулата за неговата функция на плътност — това е било направено по-рано от Моавър (фр. Abraham de Moivre).Нормалното разпределение е често използвано за опис, поне приблизително, на всяка променлива, която клони към групиране около средна стойност. Например, височините на възрастните мъже в Съединените щати са приблизително нормално разпределени, със средна аритметична стойност около 70 инча (1.8 m). Повечето мъже имат височина близка до средната, въпреки че малко число изключения имат височина значително над или под средната аритметична стойност. Хистограмата на височината на мъжете ще има формата на камбана, с все по-действителна форма, колкото повече данни са употребени.
  • A distribuição normal é uma das mais importantes distribuições da estatística, conhecida também como Distribuição de Gauss ou Gaussiana. Foi primeiramente introduzida pelo matemático Abraham de Moivre.Além de descrever uma série de fenômenos físicos e financeiros, possui grande uso na estatística inferencial. É inteiramente descrita por seus parâmetros de média e desvio padrão, ou seja, conhecendo-se estes valores consegue-se determinar qualquer probabilidade em uma distribuição Normal. Um interessante uso da Distribuição Normal é que ela serve de aproximação para o cálculo de outras distribuições quando o número de observações fica grande. Essa importante propriedade provém do Teorema do Limite Central que diz que "toda soma de variáveis aleatórias independentes de média finita e variância limitada é aproximadamente Normal, desde que o número de termos da soma seja suficientemente grande" (ver o teorema para um enunciado mais preciso).
  • Normální (nebo Gaussovo) rozdělení pravděpodobnosti je jedno z nejdůležitějších rozdělení pravděpodobnosti spojité náhodné veličiny. Slovo „normální“ zde není použito v obvyklém smyslu „obyčejné, běžné“. Jeho použití se vztahuje k staršímu významu „řídící se zákonem, předpisem nebo modelem“.Tímto rozdělením pravděpodobnosti se sice neřídí velké množství veličin, ale jeho význam spočívá v tom, že za určitých podmínek dobře aproximuje řadu jiných pravděpodobnostních rozdělení (spojitých i diskrétních).V souvislosti s normálním rozdělením jsou často zmiňovány náhodné chyby, např. chyby měření, způsobené velkým počtem neznámých a vzájemně nezávislých příčin. Proto bývá normální rozdělení také označováno jako zákon chyb. Podle tohoto zákona se také řídí rozdělení některých fyzikálních a technických veličin.
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  • Considérons une suite de variables aléatoires dont chacune est la somme d'un nombre fini de variables aléatoires avec . Pour tout , introduisons la variable aléatoire tronquée : et supposons # ; # Pour tout , et . :Alors la loi de converge vers la loi normale .
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  • Normální (nebo Gaussovo) rozdělení pravděpodobnosti je jedno z nejdůležitějších rozdělení pravděpodobnosti spojité náhodné veličiny. Slovo „normální“ zde není použito v obvyklém smyslu „obyčejné, běžné“.
  • A distribuição normal é uma das mais importantes distribuições da estatística, conhecida também como Distribuição de Gauss ou Gaussiana. Foi primeiramente introduzida pelo matemático Abraham de Moivre.Além de descrever uma série de fenômenos físicos e financeiros, possui grande uso na estatística inferencial. É inteiramente descrita por seus parâmetros de média e desvio padrão, ou seja, conhecendo-se estes valores consegue-se determinar qualquer probabilidade em uma distribuição Normal.
  • In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability that any real observation will fall between any two real limits or real numbers, as the curve approaches zero on either side.
  • В теория на вероятностите и статистиката нормалното разпределение или разпределението на Гаус e непрекъснато разпределение на вероятност, което често дава добър опис на пробите, групиращи се около средна стойност. Графиката на функцията на плътност на вероятността е с формата на камбана, с максимум в средната стойност, и е известна като функция на Гаус.
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