Template:Infobox probability distribution/doc: Difference between revisions

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{{Lua|Module:Infobox3cols|Module:InfoboxImage|Module:Check for unknown parameters}}{{TemplateStyles|Template:Infobox probability distribution/styles.css}}

=== UsageExample ===

{{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}\,\operatorname{erf}^{-1}(1/2)</math>

| aad = <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:

<syntaxhighlight lang="wikitext">

<pre>

{{Infobox probability distribution

| name =

Line 15 ⟶ 44:

| pdf =

| cdf =

| quantile =

| mean =

| median =

| mode =

| variance =

| mad =

| aad =

| skewness =

| kurtosis =

| entropy =

| cross_entropy =

| mgf =

| cf =

| pgf =

| fisher =

| moments =

| KLdiv =

| likelihood =

| JSDiv =

}}

</syntaxhighlight>

</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”"discrete" (or “mass”"mass"), “continuous”"continuous" (or “density”"density"), and “multivariate”."multivariate"

* '''{{para|pdf_image'''}} — probability density image-spec plus other text, such as: <code><nowiki>[[Image:xxx.svg|250px]]<br/>text here</nowiki></code> (optional).

* {{para|pdf_caption}} — probability density image captionn

* '''cdf_image''' — cumulative distribution image-spec plus other text, such as: <code><nowiki>[[Image:yyy.svg|250px]]<br/>text here.</nowiki></code> (optional).

* {{para|pdf_image_alt}} — [[WP:ALT|alternative text]] for the image in {{para|pdf_image}}

* '''notation''' — typical designation for this distribution, for example <math>\scriptstyle\mathcal{N}(\mu,\sigma^2)</math>. The notation should include all the distribution parameters explained in the next cell.

* '''parameters'''{{para|cdf_image}} — parameters of thecumulative distribution familyimage-spec, (such as: ''μ'' and ''σ''<supcode>2<nowiki>yyy.svg</supnowiki></code> for the normal distribution).

* {{para|cdf_caption}} — cumulative distribution image caption

* '''support''' — the support of the distribution, which may depend on the parameters. Specify this as <code><nowiki><math>x \in some set</math></nowiki></code> for continuous distributions, and as <code><nowiki><math>k \in some set</math></nowiki></code> for discrete distributions.

* {{para|cdf_image_alt}} — [[WP:ALT|alternative text]] for the image in {{para|cdf_image}}

* '''pdf''' — probability density function (or probability mass function), such as: <code><nowiki><math>\frac{\Gamma(r+k)}{k!\,\Gamma(r)}\,p^r\,(1-p)^k \!</math></nowiki></code>. Please exclude the function label, such as “''ƒ''(x;''μ'',''σ''²)”.

* '''{{para|notation'''}} — typical designation for this distribution, for example <math>\scriptstyle\mathcal{N}(\mu,\sigma^2)</math>. The notation should include all the distribution parameters explained in the next cell.

* '''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>.

* '''quantile'''{{para|parameters}} — [[quantileparameters function]]of (or inverse cumulativethe distribution function).family If <math>F()</math>such isas the CDF{{mvar|μ}} and {{math|''σ''<mathsup>Q()2</mathsup>}} isfor the quantilenormal function, then <math>Q(F(xdistribution))=x</math>.

* '''{{para|support'''}} — the support of the distribution, which may depend on the parameters. Specify this as <code><nowikisyntaxhighlight lang="tex" inline><math>x \in some set</math></nowiki></codesyntaxhighlight> for continuous distributions, and as <code><nowikisyntaxhighlight lang="tex" inline><math>k \in some set</math></nowiki></codesyntaxhighlight> for discrete distributions.

* '''mean''' — the [[mean]], or [[expected value]].

* '''{{para|pdf'''}} — probability density function (or probability mass function), such as: <code><nowikisyntaxhighlight lang="tex" inline><math>\frac{\Gamma(r+k)}{k!\,\Gamma(r)}\,p^r\,(1-p)^k \!</math></nowiki></codesyntaxhighlight>. Please exclude the function label, such as “"{{math|''ƒ''(x;&nbsp;''μ'',''σ''²)”}}".

* '''median''' — the [[median]], only for univariate distributions.

* '''{{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>.

* '''mode''' — the [[mode (statistics)|mode]].

* {{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>

* '''variance''' — [[variance]] of the distribution, or [[covariance matrix]] in multivariate case.

* '''skewness'''{{para|mean}} — the [[skewnessmean]], or [[expected value]].

* '''{{para|median'''}} — the [[median]], only for univariate distributions.

* '''kurtosis''' — the [[kurtosis excess]].

* '''entropy'''{{para|mode}} — the [[informationmode entropy(statistics)|mode]].

* '''{{para|variance'''}} — [[variance]] of the distribution, or [[covariance matrix]] in multivariate case.

* '''mgf''' — the [[moment-generating function]], for example: <code><nowiki><math>\left(\frac{p}{1-(1-p) e^t}\right)^r \!</math></nowiki></code>.

* {{para|mad}} — the [[median absolute deviation]] around the median.

* '''char''' or '''cf''' — the [[Characteristic function (probability theory)|characteristic function]], such as: <code><nowiki><math>\left(\frac{p}{1-(1-p) e^{i\,t}}\right)^r \!</math></nowiki></code>.

* {{para|aad}} — the [[average absolute deviation|mean absolute deviation]] around the mean.

* '''pgf''' - the [[Probability-generating function]].

* '''fisher'''{{para|skewness}} — the [[Fisher information matrixskewness]] for the model.

* '''{{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|cross_entropy}} — the [[cross-entropy]] of the model

* '''{{para|mgf'''}} — the [[moment-generating function]], for example: <code><nowikisyntaxhighlight lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^t}\right)^r \!</math></nowiki></codesyntaxhighlight>.

* '''{{para|char''' or '''}}/{{para|cf'''}} — the [[Characteristic function (probability theory)|characteristic function]], such as: <code><nowikisyntaxhighlight lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^{i\,tit}}\right)^r \!</math></nowiki></codesyntaxhighlight>.

* '''{{para|pgf'''}} - the [[Probabilityprobability-generating function]].

* {{para|fisher}} — the [[Fisher information matrix]] for the model.

* {{para|KLDiv}} — the [[Kullback-Leibler divergence]] of the model

* {{para|likelihood}} — the [[Likelihood function]] of the model

* {{para|JSDiv}} — the [[Jensen-Shannon divergence]] of the model

* {{para|moments}} — formulas to use in [[Method of moments (statistics)|method of moments]] for the model.

* {{para|ES}} — the [[expected shortfall]] or CVaR for the model.

* {{para|bPOE}} — the buffered probability of exceedance for 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).

{{para|parameters2}}, {{para|support2}}, {{para|pdf2}}, {{para|cdf2}}, {{para|mean2}}, {{para|median2}}, {{para|mode2}}, {{para|variance2}}, {{para|mad}}, {{para|aad}}, {{para|skewness2}}, {{para|kurtosis2}}, {{para|entropy2}}, {{para|mgf2}}, {{para|char2}}/{{para|cf2}}, {{para|moments2}}, {{para|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]].

* '''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).

=== SeeTracking alsocategory ===

* {{clc|Pages using infobox probability distribution with unknown parameters}}

* [[WP:Infobox]]

* Talk page: [[Template talk:Probability distribution]]

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