Template:Infobox probability distribution
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Example
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Probability density function File:Normal Distribution PDF.svgThe red curve is the standard normal distribution | |||
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Cumulative distribution function File:Normal Distribution CDF.svg | |||
| Notation | <math>\mathcal{N}(\mu,\sigma^2)</math> | ||
|---|---|---|---|
| Parameters |
<math>\mu\in\R</math> = mean (location) <math>\sigma^2>0</math> = variance (squared scale) | ||
| Support | <math>x\in\R</math> | ||
| <math>\frac{1}{\sigma\sqrt{2\pi | |||
| 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>
| 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>
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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: <syntaxhighlight lang="wikitext">
</syntaxhighlight>
Parameters
|name=— Name at the top of the infobox; should be the name of the distribution without the word "distribution" in it, e.g. "Normal", "Exponential" (optional)|type=— possible values are "discrete" (or "mass"), "continuous" (or "density"), and "multivariate"|pdf_image=— probability density image-spec, such as:xxx.svg.|pdf_caption=— probability density image caption|pdf_image_alt=— alternative text for the image in|pdf_image=|cdf_image=— cumulative distribution image-spec, such as:yyy.svg.|cdf_caption=— cumulative distribution image caption|cdf_image_alt=— alternative text for the image in|cdf_image=|notation=— typical designation for this distribution, for example <math>\mathcal{N}(\mu,\sigma^2)</math>. The notation should include all the distribution parameters explained in the next cell.|parameters=— parameters of the distribution family (such as μ and σ2 for the normal distribution).|support=— the support of the distribution, which may depend on the parameters. Specify this as <syntaxhighlight lang="tex" inline><math>x \in some set</math></syntaxhighlight> for continuous distributions, and as <syntaxhighlight lang="tex" inline><math>k \in some set</math></syntaxhighlight> for discrete distributions.|pdf=— probability density function (or probability mass function), such as: <syntaxhighlight lang="tex" inline><math>\frac{\Gamma(r+k)}{k!\Gamma(r)}p^r(1-p)^k</math></syntaxhighlight>. Please exclude the function label, such as "ƒ(x; μ,σ2)".|cdf=— cumulative distribution function, e.g.:<math>I_p(r,k+1)\text{ where }I_p(x,y)</math> is the [[regularized incomplete beta function]].|quantile=— quantile function (or inverse cumulative distribution function). If <math>F()</math> is the CDF and <math>Q()</math> is the quantile function, then <math>Q(F(x))=x</math>|mean=— the mean, or expected value.|median=— the median, only for univariate distributions.|mode=— the mode.|variance=— variance of the distribution, or covariance matrix in multivariate case.|mad=— the mean absolute deviation.|skewness=— the skewness.|kurtosis=— the kurtosis excess.|entropy=— the differential information entropy, preferably expressed in unspecified units using base-unspecific log(.) rather than base-specific ln(.) which yields entropy in units of nats only.|cross_entropy=— the Cross entropy of the model|mgf=— the moment-generating function, for example: <syntaxhighlight lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^t}\right)^r</math></syntaxhighlight>.|char=/|cf=— the characteristic function, such as: <syntaxhighlight lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^{it}}\right)^r</math></syntaxhighlight>.|pgf=- the Probability-generating function.|fisher=— the Fisher information matrix for the model.|KLDiv=— the Kullback-Leibler divergence of the model|JSDiv=— the Jensen-Shannon divergence of the model|moments=— formulas to use in Method of moments for the model.|ES=— the Expected shortfall or CVaR for the model.|bPOE=— the Buffered Probability of Exceedance for the model.|intro=— optional message which will be displayed before all other content in the infobox.|marginleft=— margin space left of infobox (default: 1em).|box_width=— width of the infobox (default: 325px).
|parameters2=, |support2=, |pdf2=, |cdf2=, |mean2=, |median2=, |mode2=, |variance2=, |mad=, |skewness2=, |kurtosis2=, |entropy2=, |mgf2=, |char2=/|cf2=, |moments2=, |fisher2= are the same as their counterparts above. They should be used when the distribution needs two sets to describe it, e.g. Gamma distribution.
