What is the name for a non-normalized distribution? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T17:13:56Z http://mathoverflow.net/feeds/question/107117 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/107117/what-is-the-name-for-a-non-normalized-distribution What is the name for a non-normalized distribution? Scot Free Kennedy 2012-09-13T19:23:41Z 2012-09-17T09:59:28Z <p>For some analysis work with probability distributions, I remember a common trick being to drop the "integrate to 1" requirement, so the set becomes closed under addition and is more convenient to work with in general. It's always easy to re-normalize at the end, if needed.</p> <p>I cannot for the life of me remember what these more general objects are called, though. Are they just "distributions" or is there a more specific name? Again, the name for the members of a function space with all the properties of a PDF except the requirement that they integrate to 1.</p> http://mathoverflow.net/questions/107117/what-is-the-name-for-a-non-normalized-distribution/107123#107123 Answer by Adrien for What is the name for a non-normalized distribution? Adrien 2012-09-13T20:20:15Z 2012-09-13T20:20:15Z <p>Measures ? They are also more restrictive subsets of measure like finite measures or $\sigma$-finite measures.</p> http://mathoverflow.net/questions/107117/what-is-the-name-for-a-non-normalized-distribution/107125#107125 Answer by an12 for What is the name for a non-normalized distribution? an12 2012-09-13T21:13:57Z 2012-09-13T22:37:01Z <p>The name is "kernel of a probability distribution" or "unnormalized kernel". This usage seems to be mostly prevalent in Bayesian Statistics as explained here</p> <blockquote> <p><a href="http://en.wikipedia.org/wiki/Kernel_%28statistics%29" rel="nofollow">http://en.wikipedia.org/wiki/Kernel_(statistics)</a></p> </blockquote> http://mathoverflow.net/questions/107117/what-is-the-name-for-a-non-normalized-distribution/107370#107370 Answer by Adrien Hardy for What is the name for a non-normalized distribution? Adrien Hardy 2012-09-17T09:59:28Z 2012-09-17T09:59:28Z <p>For an absolutely continuous finite Borel measure $\mu(dx)=f(x)dx$ on $\mathbb R$, if $\mu(\mathbb R)\neq 1$ then $f$ is sometimes called the "intensity" of the measure. </p>