Template:Infobox probability distribution/sandbox

Normal distribution
	Probability density function The red curve is the standard normal distribution
	Cumulative distribution function
Notation
Parameters	= mean (location); = variance (squared scale)
Support
PDF
CDF
Quantile
Mean
Median
Mode
Variance
MAD
AAD
Skewness
Excess kurtosis
Entropy
MGF
CF
Fisher information
Kullback–Leibler divergence

This is the template sandbox page for Template:Infobox probability distribution (diff).
See also the companion subpage for test cases.

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Example

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:

{{Infobox probability distribution
| name       = 
| type       = 
| pdf_image  = 
| cdf_image  = 
| notation   = 
| parameters = 
| support    = 
| pdf        = 
| cdf        = 
| quantile   = 
| mean       = 
| median     = 
| mode       = 
| variance   = 
| mad        =
| aad        = 
| skewness   = 
| kurtosis   = 
| entropy    = 
| cross_entropy = 
| mgf        = 
| cf         = 
| pgf        = 
| fisher     = 
| moments    = 
| KLdiv      = 
| JSDiv      = 
}}

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 ${\mathcal {N}}(\mu ,\sigma ^{2})$ . The notation should include all the distribution parameters explained in the next cell.
|parameters= — parameters of the distribution family (such as $μ$ and $σ 2$ for the normal distribution).
|support= — the support of the distribution, which may depend on the parameters. Specify this as <math>x \in some set</math> for continuous distributions, and as <math>k \in some set</math> for discrete distributions.
|pdf= — probability density function (or probability mass function), such as: <math>\frac{\Gamma(r+k)}{k!\Gamma(r)}p^r(1-p)^k</math>. Please exclude the function label, such as " $ƒ (x; μ, σ 2)$ ".
|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 $F()$ is the CDF and $Q()$ is the quantile function, then $Q(F(x))=x$
|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 median absolute deviation around the median.
|aad= — the mean absolute deviation around the mean.
|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: <math>\left(\frac{p}{1-(1-p) e^t}\right)^r</math>.
|char=/|cf= — the characteristic function, such as: <math>\left(\frac{p}{1-(1-p) e^{it}}\right)^r</math>.
|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).

Tracking category

Category:Pages using infobox probability distribution with unknown parameters (0)

The above documentation is transcluded from Template:Infobox probability distribution/doc.
Editors can experiment in this template's sandbox and testcases pages.
Add categories to the /doc subpage. Subpages of this template.

Probability density function The red curve is the standard normal distribution
Cumulative distribution function
Notation	${\mathcal {N}}(\mu ,\sigma ^{2})$
Parameters	$\mu \in \mathbb {R}$ = mean (location) $\sigma ^{2}>0$ = variance (squared scale)
Support	$x\in \mathbb {R}$
PDF	${\frac {1}{\sigma {\sqrt {2\pi }}}}e^{-{\frac {1}{2}}\left({\frac {x-\mu }{\sigma }}\right)^{2}}$
CDF	${\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sigma {\sqrt {2}}}}\right)\right]$
Quantile	$\mu +\sigma {\sqrt {2}}\operatorname {erf} ^{-1}(2p-1)$
Mean	$\mu$
Median	$\mu$
Mode	$\mu$
Variance	$\sigma ^{2}$
MAD	$\sigma {\sqrt {2}}\,\operatorname {erf} ^{-1}(1/2)$
AAD	$\sigma {\sqrt {2/\pi }}$
Skewness	$0$
Excess kurtosis	$0$
Entropy	${\frac {1}{2}}\log(2\pi e\sigma ^{2})$
MGF	$\exp(\mu t+\sigma ^{2}t^{2}/2)$
CF	$\exp(i\mu t-\sigma ^{2}t^{2}/2)$
Fisher information	${\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}$ ${\mathcal {I}}(\mu ,\sigma ^{2})={\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}$
Kullback–Leibler divergence	${1 \over 2}\left\{\left({\frac {\sigma _{0}}{\sigma _{1}}}\right)^{2}+{\frac {(\mu _{1}-\mu _{0})^{2}}{\sigma _{1}^{2}}}-1+2\ln {\sigma _{1} \over \sigma _{0}}\right\}$