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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:
<pre>
| pdf =
| cdf =
| quantile =
| mean =
| median =
| mgf =
| cf =
| pgf =
| fisher =
| KLdiv =
| JSDiv =
}}
</pre>
==== Parameters ====
* '''{{para|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).
* '''{{para|type'''}} — possible values are “discrete” (or “mass”), “continuous” (or “density”), and “multivariate”.
* '''{{para|pdf_image'''}} — probability density image-spec, such as: <code><nowiki>xxx.svg</nowiki></code>.
* '''{{para|pdf_caption'''}} — probability density image caption
* '''{{para|cdf_image'''}} — cumulative distribution image-spec, such as: <code><nowiki>yyy.svg</nowiki></code>.
* '''{{para|cdf_caption'''}} — cumulative distribution image caption
* '''{{para|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.
* '''{{para|parameters'''}} — parameters of the distribution family (such as {{mvar|μ}} and {{math|''σ''<sup>2</sup>}} for the normal distribution).
* '''{{para|support'''}} — the support of the distribution, which may depend on the parameters. Specify this as <source lang="tex" inline><math>x \in some set</math></source> for continuous distributions, and as <source lang="tex" inline><math>k \in some set</math></source> for discrete distributions.
* '''{{para|pdf'''}} — probability density function (or probability mass function), such as: <source lang="tex" inline><math>\frac{\Gamma(r+k)}{k!\Gamma(r)}p^r(1-p)^k</math></source>. Please exclude the function label, such as “{{math|''ƒ''(x; ''μ'',''σ''<sup>2</sup>)}}”.
* '''{{para|cdf'''}} — cumulative distribution function, e.g.: <code><nowiki><math>I_p(r,k+1)\text{ where }I_p(x,y)</math> is the [[regularized incomplete beta function]]</nowiki></code>.
* '''{{para|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>
* '''{{para|mean'''}} — the [[mean]], or [[expected value]].
* '''{{para|median'''}} — the [[median]], only for univariate distributions.
* '''{{para|mode'''}} — the [[mode (statistics)|mode]].
* '''{{para|variance'''}} — [[variance]] of the distribution, or [[covariance matrix]] in multivariate case.
* '''{{para|skewness'''}} — the [[skewness]].
* '''{{para|kurtosis'''}} — the [[kurtosis excess]].
* '''{{para|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.
* '''{{para|mgf'''}} — the [[moment-generating function]], for example: <source lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^t}\right)^r</math></source>.
* '''{{para|char'''}} or '''{{para|cf'''}} — the [[Characteristic function (probability theory)|characteristic function]], such as: <source lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^{it}}\right)^r</math></source>.
* '''{{para|pgf'''}} - the [[Probability-generating function]].
* '''{{para|fisher'''}} — the [[Fisher information matrix]] for the model.
* '''{{para|KLDiv'''}} — the [[Kullback-Leibler divergence]] of the model
* '''{{para|JSDiv'''}} — the [[Jensen-Shannon divergence]] of the model
* '''{{para|intro '''}} — optional message which will be displayed before all other content in the infobox. ▼* '''{{para|marginleft '''}} — margin space left of infobox (default: 1em). ▼* '''{{para|box_width '''}} — width of the infobox (default: 325px). ▼
▲* '''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).
* [[Template:Infobox probability distribution 2]] – for distributions with two different sets of parameters
* [[WP:Infobox]]
* Talk page: [[Template talk:Probability distribution]]
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[[Category:Mathematics infobox templates|{{PAGENAME}}]]
[[Category:Statistics templates]]
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