Difference between revisions of "Template:Infobox probability distribution"

From blackwiki
Jump to navigation Jump to search
imported>Qwfp
(Undid revision 199391467 by Sohale Sorry but that looks odd on the pages that use this template unless you fill in the info for all or know how to fix template.)
imported>DinoD123
(made PMF be in all caps)
 
(48 intermediate revisions by 29 users not shown)
Line 1: Line 1:
{| class="infobox bordered wikitable" style="width: 325px; font-size: 95%; margin-left: 1em; margin-bottom: 0.5em;"
+
{{infobox3cols
|+ {{{name}}}
+
| bodyclass      = bordered
|- style="text-align: center;"
+
| bodystyle      = width: {{{box_width|325px}}}; max-width: {{{box_width|325px}}}; font-size: 95%;
| colspan="2" | Probability {{{type}}} function<br />{{{pdf_image}}}
+
 
|- style="text-align: center;"
+
| title          = {{{name|}}}
| colspan="2" | Cumulative distribution function<br />{{{cdf_image}}}
+
| subheaderstyle = text-align:left;
|- valign="top"
+
| subheader      =  {{{intro|}}}
! Parameters
+
 
| {{{parameters}}}
+
| image1        = {{#if: {{{pdf_image|}}}|<div>{{#switch: {{{type|<noinclude>discrete</noinclude>}}} | discrete | mass = Probability mass function | multivariate | continuous | density = Probability density function }}</div>{{#invoke:InfoboxImage|InfoboxImage|image={{{pdf_image}}}|alt={{{pdf_image_alt|}}}}}}}
|-
+
| caption1      = {{{pdf_caption|}}}
! [[Support (mathematics)|Support]]
+
 
| {{{support}}}
+
| image2        = {{#if: {{{cdf_image|}}}|<div>Cumulative distribution function</div>{{#invoke:InfoboxImage|InfoboxImage|image={{{cdf_image}}}|alt={{{cdf_image_alt|}}}}}}}
|-
+
| caption2      = {{{cdf_caption|}}}
! {{Probability distribution/link {{{type}}}}}
+
 
| {{{pdf}}}
+
| label1        = Notation
|-
+
| data1          = {{{notation|}}}
! [[Cumulative distribution function]] (cdf)
+
 
| {{{cdf}}}
+
| label2        = Parameters
|-
+
| data2          = {{#if: {{{parameters2|}}} | | {{{parameters|}}} }}
! [[expected value|Mean]]
+
| data2a        = {{{parameters|}}}
| {{{mean}}}
+
| data2b        = {{{parameters2|}}}
|-
+
 
! [[Median]]
+
| label3        = [[Support (mathematics)|Support]]
| {{{median}}}
+
| data3          = {{#if: {{{support2|}}} | | {{{support|}}} }}
|-
+
| data3a        = {{{support|}}}
! [[Mode (statistics)|Mode]]
+
| data3b        = {{{support2|}}}
| {{{mode}}}
+
 
|-
+
| label4        = {{#switch: {{{type|<noinclude>discrete</noinclude>}}}
! [[Variance]]
+
                  | discrete | mass = [[Probability mass function|PMF]]
| {{{variance}}}
+
                  | multivariate | continuous | density = [[Probability density function|PDF]]
|-
+
                  | #default = {{Error|Unknown type}}
! [[Skewness]]
+
                  }}
| {{{skewness}}}
+
| data4          = {{#if: {{{pdf2|}}} | | {{{pdf|}}} }}
|-
+
| data4a        = {{{pdf|}}}
! Excess [[kurtosis]]
+
| data4b        = {{{pdf2|}}}
| {{{kurtosis}}}
+
 
|-
+
| label5        = [[Cumulative distribution function|CDF]]
! [[Information entropy|Entropy]]
+
| data5          = {{#if: {{{cdf2|}}} | | {{{cdf|}}} }}
| {{{entropy}}}
+
| data5a        = {{{cdf|}}}
|-
+
| data5b        = {{{cdf2|}}}
! [[Moment-generating function]] (mgf)
+
 
| {{{mgf}}}
+
| label6        = [[Quantile function|Quantile]]
|-
+
| data6          = {{{quantile|}}}
! [[Characteristic function (probability theory)|Characteristic function]]
+
 
| {{{char}}}
+
| label7        = [[Expected value|Mean]]
|}<noinclude>
+
| data7          = {{#if: {{{mean2|}}} | | {{{mean|}}} }}
[[zh:Template:機率分佈]]
+
| data7a        = {{{mean|}}}
 +
| data7b        = {{{mean2|}}}
 +
 
 +
| label8        = [[Median]]
 +
| data8          = {{#if: {{{median2|}}} | | {{{median|}}} }}
 +
| data8a        = {{{median|}}}
 +
| data8b        = {{{median2|}}}
 +
 
 +
| label9        = [[Mode (statistics)|Mode]]
 +
| data9          = {{#if: {{{mode2|}}} | | {{{mode|}}} }}
 +
| data9a        = {{{mode|}}}
 +
| data9b        = {{{mode2|}}}
 +
 
 +
| label10        = {{#switch: {{{type|<noinclude>discrete</noinclude>}}}
 +
                  | discrete | continuous | mass | density = [[Variance]]
 +
                  | multivariate = [[Covariance matrix|Variance]]
 +
                  | #default = {{Error|Unknown type}}
 +
                  }}
 +
| data10        = {{#if: {{{variance2|}}} | | {{{variance|}}} }}
 +
| data10a        = {{{variance|}}}
 +
| data10b        = {{{variance2|}}}
 +
 
 +
| label11        = [[average absolute deviation|MAD]]
 +
| data11        = {{#if: {{{mad2|}}} | | {{{mad|}}} }}
 +
| data11a        = {{{mad|}}}
 +
| data11b        = {{{mad2|}}}
 +
 
 +
| label12        = [[Skewness]]
 +
| data12        = {{#if: {{{skewness2|}}} | | {{{skewness|}}} }}
 +
| data12a        = {{{skewness|}}}
 +
| data12b        = {{{skewness2|}}}
 +
 
 +
| label13        = [[Excess kurtosis|Ex. kurtosis]]
 +
| data13        = {{#if: {{{kurtosis2|}}} | | {{{kurtosis|}}} }}
 +
| data13a        = {{{kurtosis|}}}
 +
| data13b        = {{{kurtosis2|}}}
 +
 
 +
| label14        = [[Information entropy|Entropy]]
 +
| data14        = {{#if: {{{entropy2|}}} | | {{{entropy|}}} }}
 +
| data14a        = {{{entropy|}}}
 +
| data14b        = {{{entropy2|}}}
 +
 
 +
| label15        = [[Moment-generating function|MGF]]
 +
| data15        = {{#if: {{{mgf2|}}} | | {{{mgf|}}} }}
 +
| data15a        = {{{mgf|}}}
 +
| data15b        = {{{mgf2|}}}
 +
 
 +
| label16        = [[Characteristic function (probability theory)|CF]]
 +
| data16        = {{#if: {{{char2|{{{cf2|}}}}}} | | {{{char|{{{cf|}}}}}} }}
 +
| data16a        = {{{char|{{{cf|}}}}}}
 +
| data16b        = {{{char2|{{{cf2|}}}}}}
 +
 
 +
| label17        = [[Probability-generating function|PGF]]
 +
| data17        = {{{pgf|}}}
 +
 
 +
| label18        = [[Fisher information]]
 +
| data18        = {{{fisher|}}}
 +
 
 +
| label19        = [[Kullback-Leibler divergence]]
 +
| data19        = {{{KLDiv|}}}
 +
 
 +
| label20        = [[Jensen-Shannon divergence]]
 +
| data20        = {{{JSDdiv|}}}
 +
 
 +
| label21        = [[Method of moments (statistics)|Method of Moments]]
 +
| data21        = {{#if: {{{moments2|}}} | | {{{moments|}}} }}
 +
| data21a        = {{{moments|}}}
 +
| data21b        = {{{moments2|}}}
 +
 
 +
}}{{#invoke:Check for unknown parameters|check|unknown={{main other|[[Category:Pages using infobox probability distribution with unknown parameters|_VALUE_{{PAGENAME}}]]}}|preview=Page using [[Template:Infobox probability distribution]] with unknown parameter "_VALUE_"|ignoreblank=y| box_width | cdf | cdf_caption | cdf_image | cdf_image_alt | cdf2 | cf | cf2 | char | char2 | entropy | entropy2 | fisher | intro | JSDdiv | KLDiv | kurtosis | kurtosis2 | mad | mad2 | mean | mean2 | median | median2 | mgf | mgf2 | mode | mode2 | moments | moments2 | name | notation | parameters | parameters2 | pdf | pdf_caption | pdf_image | pdf_image_alt | pdf2 | pgf | quantile | skewness | skewness2 | support | support2 | type | variance | variance2 }}<noinclude>
 +
{{Documentation}}
 
</noinclude>
 
</noinclude>

Latest revision as of 17:44, 31 August 2020

[[Category:Infobox templates|Template:Remove first word ]]

Template documentation[view] [edit] [history] [purge]

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    = 
| 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 <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 Template:Mvar 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 <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.
  • |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.
  • |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=, and |moments2= are the same as their counterparts above. They should be used when the distribution needs two sets to describe it, e.g. Gamma distribution.

Tracking category