![](https://upload.wikimedia.org/wikipedia/commons/thumb/4/43/Test_Template_Info-Icon_-_Version_%282%29.svg/50px-Test_Template_Info-Icon_-_Version_%282%29.svg.png)
Example
Probability density function ![]() The red curve is the standard normal distribution | |||
Cumulative distribution function ![]() | |||
Notation | |||
---|---|---|---|
Parameters |
= mean (location) = variance (squared scale) | ||
Support | |||
CDF | |||
Quantile | |||
Mean | |||
Median | |||
Mode | |||
Variance | |||
MAD | |||
Skewness | |||
Excess kurtosis | |||
Entropy | |||
MGF | |||
CF | |||
Fisher information |
| ||
Kullback–Leibler divergence |
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 =
| 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 . 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<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,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 is the CDF and is the quantile function, then|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 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).
|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.