Gaussiska

Gaussiska refers to the Gaussian or normal distribution in statistics, and to related concepts derived from Carl Friedrich Gauss’s work. It is a continuous probability distribution that is symmetric, bell-shaped, and fully described by two parameters: the mean μ, which determines its center, and the standard deviation σ, which controls its spread. The Gaussian distribution is widely used to model natural phenomena and measurement errors because many small, independent effects tend to combine to produce a bell curve.

The probability density function of a Gaussian distribution is f(x) = (1/(σ√(2π))) exp(-(x-μ)²/(2σ²)). Key properties include: the mean, median, and mode all equal μ; the distribution is fully determined by μ and σ; it is closed under linear transformations and, importantly, the sum of independent Gaussian variables is also Gaussian. The standard normal distribution is the special case with μ = 0 and σ = 1; any Gaussian can be obtained from the standard normal by scaling and shifting.

Historically, the normal distribution gained its name through its connection to probability and least squares. Although de Moivre studied similar forms, the term "Gaussian" honors Gauss for his development of methods used to model measurement errors and his contributions to statistical theory. The Gaussiska concept thus underpins much of classical statistics, hypothesis testing, estimation, and data modeling, and it remains central in theories of probability and inference due to the Central Limit Theorem.