Template:Infobox probability distribution/doc: Difference between revisions

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<!-- PLEASE ADD CATEGORIES AT THE BOTTOM OF THIS PAGE -->
{{Lua|Module:Infobox|Module:InfoboxImage|Module:Check for unknown parameters}}
== Example ==
 
{{Infobox probability distribution
| name = Normal distribution
| type = density
| pdf_image = Normal Distribution PDF.svg
| pdf_caption = The red curve is the ''standard normal distribution''
| cdf_image = Normal Distribution CDF.svg
| cdf_caption =
| notation = <math>\mathcal{N}(\mu,\sigma^2)</math>
| parameters = <math>\mu\in\R</math> = mean ([[___location parameter|___location]])<br /><math>\sigma^2>0</math> = variance (squared [[scale parameter|scale]])
| support = <math>x\in\R</math>
| pdf = <math>\frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x - \mu}{\sigma}\right)^2}</math>
| cdf = <math>\frac{1}{2}\left[1 + \operatorname{erf}\left( \frac{x-\mu}{\sigma\sqrt{2}}\right)\right] </math>
| quantile = <math>\mu+\sigma\sqrt{2} \operatorname{erf}^{-1}(2p-1)</math>
| mean = <math>\mu</math>
| median = <math>\mu</math>
| mode = <math>\mu</math>
| variance = <math>\sigma^2</math>
| mad = <math>\sigma\sqrt{2/\pi}</math>
| skewness = <math>0</math>
| kurtosis = <math>0</math> <!-- DO NOT REPLACE THIS WITH THE OLD-STYLE KURTOSIS WHICH IS 3. -->
| entropy = <math>\frac{1}{2} \log(2\pi e\sigma^2)</math>
| mgf = <math>\exp(\mu t + \sigma^2t^2/2)</math>
| char = <math>\exp(i\mu t - \sigma^2 t^2/2)</math>
| fisher = <math>\mathcal{I}(\mu,\sigma) =\begin {pmatrix} 1/\sigma^2 & 0 \\ 0 & 2/\sigma^2\end{pmatrix}</math>
<math>\mathcal{I}(\mu,\sigma^2) =\begin {pmatrix} 1/\sigma^2 & 0 \\ 0 & 1/(2\sigma^4)\end{pmatrix}</math>
| KLDiv = <math>{ 1 \over 2 } \left\{ \left( \frac{\sigma_0}{\sigma_1} \right)^2 + \frac{(\mu_1 - \mu_0)^2}{\sigma_1^2} - 1 + 2 \ln {\sigma_1 \over \sigma_0} \right\}</math>
}}
== Usage ==
The '''Template:Infobox probability distribution''' generates a right-hand side infobox, based on the specified parameters. To use this template, copy the following code in your article and fill in as appropriate: