Editing Hubbert curve (section)

==Shape==
[[Image:Hubbert curve.svg|thumb|Plot of the Hubbert curve]]
The prototypical Hubbert curve is a [[probability density function]] of a [[logistic distribution]] curve. It is not a [[gaussian function]] (which is used to plot [[normal distribution]]s), but the two have a similar appearance. The density of a  Hubbert curve approaches zero more slowly than a gaussian function:

:<math>
x = {e^{-t}\over(1+e^{-t})^2}={1\over2+2\cosh t}={1\over4}\operatorname{sech}^{2} {t\over2}.
</math>

The graph of a Hubbert curve consists of three key elements: 
# a gradual rise from zero resource production that then increases quickly
# a "[[Hubbert peak theory|Hubbert peak]]", representing the maximum production level
# a drop from the peak that then follows a steep production decline.

The actual shape of a graph of real world production trends is determined by various factors, such as development of enhanced production techniques, availability of competing resources, and government regulations on production or consumption.  Because of such factors, real world Hubbert curves are often not symmetrical.