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Normal Distribution

\begin{figure}\begin{center}\BoxedEPSF{NormalDistribution.epsf scaled 650}\end{center}\end{figure}

Another name for a Gaussian Distribution. Given a normal distribution in a Variate $x$ with Mean $\mu$ and Variance $\sigma^2$,

P(x)\,dx={1\over \sigma\sqrt{2\pi}} e^{-(x-\mu)^2/2\sigma^2}\,dx,

the so-called ``Standard Normal Distribution'' is given by taking $\mu=0$ and $\sigma^2=1$. An arbitrary normal distribution can be converted to a Standard Normal Distribution by changing variables to $z\equiv (x-\mu)/\sigma$, so $dz=dx/\sigma$, yielding

P(x)\,dx = {1\over\sqrt{2\pi}} e^{-z^2/2}\,dz.

The Fisher-Behrens Problem is the determination of a test for the equality of Means for two normal distributions with different Variances.

See also Fisher-Behrens Problem, Gaussian Distribution, Half-Normal Distribution, Kolmogorov-Smirnov Test, Normal Distribution Function, Standard Normal Distribution, Tetrachoric Function

© 1996-9 Eric W. Weisstein