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Definition 2025

normal distribution ‎(plural normal distributions)

(statistics) Any of a family of continuous probability distributions such that the probability density function is the Gaussian function
$\varphi _{\mu ,\sigma ^{2}}(x)={\frac {1}{\sigma {\sqrt {2\pi }}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}={\frac {1}{\sigma }}\varphi \left({\frac {x-\mu }{\sigma }}\right),\quad x\in \mathbb {R}$

probability distribution