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• Normal_distribution abstract "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.".
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• Normal_distribution name "Normal".
• Normal_distribution parameters "— mean".
• Normal_distribution parameters "— variance".
• Normal_distribution pdfImage "(The red curve is the standard normal distribution)".
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• Normal_distribution title "Normal Distribution".
• Normal_distribution title "Normal distribution".
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• Normal_distribution subject Category:Conjugate_prior_distributions.
• Normal_distribution subject Category:Continuous_distributions.
• Normal_distribution subject Category:Distributions_with_conjugate_priors.
• Normal_distribution subject Category:Exponential_family_distributions.
• Normal_distribution subject Category:Normal_distribution.
• Normal_distribution subject Category:Probability_distributions.
• Normal_distribution subject Category:Stable_distributions.
• Normal_distribution comment "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_distribution label "Distribución normal".
• Normal_distribution label "Distribuição normal".
• Normal_distribution label "Distribuzione normale".
• Normal_distribution label "Loi normale".
• Normal_distribution label "Normal distribution".
• Normal_distribution label "Normale verdeling".
• Normal_distribution label "Normalverteilung".
• Normal_distribution label "Rozkład normalny".
• Normal_distribution label "Нормальное распределение".
• Normal_distribution label "توزيع احتمالي طبيعي".
• Normal_distribution label "正态分布".
• Normal_distribution label "正規分布".
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• Normal_distribution sameAs 正規分布.
• Normal_distribution sameAs 정규분포.
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