Template:Infobox probability distribution/doc: Difference between revisions

Revision as of 06:12, 26 July 2017

Revision as of 03:27, 25 September 2017

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* '''cdf_image''' — cumulative distribution image-spec, such as: <code><nowiki>yyy.svg</nowiki></code>.

* '''cdf_caption''' — cumulative distribution image caption

* '''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''' — parameters of the distribution family (such as {{mvar|μ}} and {{math|''σ''²}} for the normal distribution).

* '''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.

* '''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;&nbsp;''μ'',''σ''²)}}”.

* '''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''' — [[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>

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* '''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: <source lang="tex" inline><math>\left(\frac{p}{1-(1-p) e^t}\right)^r \!</math></source>.

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

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

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