Hubbert curve

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The Hubbert curve, named after the geophysicist M. King Hubbert, is the derivative of the logistic function.

An example of a Hubbert curve is:

x = {e^{-t}\over(1+e^{-t})^2}={1\over2+2\cosh t}

Plot of the Hubbert curve

The Hubbert curve has some resemblance to, but is different from, the shape of the probability density function of the normal distribution. It was popularised as a model of the rate of petroleum extraction. According to this model, the rate of production of oil is determined by the rate of new oil well discovery; a "Hubbert peak" in the oil extraction rate will thus be followed by a gradual decline of oil production.

For more information on petroleum exhaustion, see the Hubbert peak theory article.

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