Difference between revisions of "Normal cdf"
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(Created page with "The normal cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by $$F(x) = \dfrac{1}{2} \le...") |
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The normal [[cumulative distribution function]] $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by | The normal [[cumulative distribution function]] $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by | ||
| − | $$F(x) = \dfrac{1}{2} \left[ 1 + \erf \left( \dfrac{x-\mu}{\sigma \sqrt{2}} \right) \right],$$ | + | $$F(x) = \dfrac{1}{2} \left[ 1 + \mathrm{erf} \left( \dfrac{x-\mu}{\sigma \sqrt{2}} \right) \right],$$ |
| − | where $\erf$ denotes the [[error]] function and $\exp$ denotes the [[exponential]] function. | + | where $\mathrm{erf}$ denotes the [[error]] function and $\exp$ denotes the [[exponential]] function. |
=Properties= | =Properties= | ||
Latest revision as of 03:26, 12 March 2018
The normal cumulative distribution function $F \colon \mathbb{R} \rightarrow \mathbb{R}$ is defined for $\mu \in \mathbb{R}$ and $\sigma^2 >0$ by $$F(x) = \dfrac{1}{2} \left[ 1 + \mathrm{erf} \left( \dfrac{x-\mu}{\sigma \sqrt{2}} \right) \right],$$ where $\mathrm{erf}$ denotes the error function and $\exp$ denotes the exponential function.
