Normal Distribution

Distribution Analyses

Normal Distribution

The normal distribution has the probability density function

$f(y) = \frac{1}{\sqrt{2{\pi}} \sigma } \exp( - \frac{1}2 (\frac{y-\mu}{\sigma})^2 ) {for -\infty\lt y\lt\infty}$

where $\mu$ is the mean and $\sigma$ is the scale parameter.

The cumulative distribution function is

$F(y) = \Phi( \frac{y-\mu}{\sigma} )$

where the function $\Phi$ is the cumulative distribution function of the standard normal variable: $\Phi(z) = \frac{1}{\sqrt{2{\pi}} } \int_{-\infty}^z{\exp( - u^2/2 ) du}$

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