Template:Infobox probability distribution/doc: Difference between revisions

Revision as of 00:52, 11 June 2014

Revision as of 22:31, 5 September 2015

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==== Parameters ====

* '''name''' — Name at the top of the infobox; should be the name of the distribution without the word "distribution" in it, ege.g. "Normal", "Exponential" (optional).

* '''type''' — possible values are “discrete” (or “mass”), “continuous” (or “density”), and “multivariate”.

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

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* '''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.

* '''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)”.

* '''cdf''' — cumulative distribution function, ege.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''' — [[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]].

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* '''entropy''' — the [[information entropy]].

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

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

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

* '''fisher''' — the [[Fisher information matrix]] for the model.