13 Facts About Normal distribution

In statistics, a normal distribution is a type of continuous probability distribution for a real-valued random variable.

Univariate probability distribution is generalized for vectors in the multivariate normal distribution and for matrices in the matrix normal distribution.

Every normal distribution is a version of the standard normal distribution, whose domain has been stretched by a factor and then translated by :.

CDF of the standard normal distribution can be expanded by Integration by parts into a series:.

The quantile function of the standard normal distribution is called the probit function, and can be expressed in terms of the inverse error function:.

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Geary has shown, assuming that the mean and variance are finite, that the normal distribution is the only distribution where the mean and variance calculated from a set of independent draws are independent of each other.

The normal distribution is symmetric about its mean, and is non-zero over the entire real line.

In those cases, a more heavy-tailed Normal distribution should be assumed and the appropriate robust statistical inference methods applied.

In particular, the standard normal distribution is an eigenfunction of the Fourier transform.

Any positive integer, any normal distribution with mean and variance is the distribution of the sum of independent normal deviates, each with mean and variance.

In other words, the posterior distribution has the form of a product of a normal distribution over p times an inverse gamma distribution over p, with parameters that are the same as the update equations above.

Normal distribution's works remained largely unnoticed by the scientific community, until in 1871 they were exhumed by Abbe.

Since its introduction, the normal distribution has been known by many different names: the law of error, the law of facility of errors, Laplace's second law, Gaussian law, etc.