Talk:Hubbert curve

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Steve: Sorry if I've unwittingly breached etiquette, but I've moved your comment over to Talk:M. King Hubbert when I shifted the content you were referring to. Hope you don't mind.

Previously this page started talking about the mathematical curve, but then drifted off into a discusion of petroleum production and social consequences. I've shifted the latter material over to M. King Hubbert, and slightly tidied up what's left.

Stuart

Doesn't this page duplicate the info in Peak Oil????

--GPoss 13:00, Jul 22, 2004 (UTC)

[edit] Hubbert peak theory

Discussion that might be relevant to this article is going on at Talk:Hubbert peak theory.

22:09, 6 June 2006 (UTC)

[edit] The differential equations

Most of the content here is based on the alternative method Hubbert presented in the '86 paper. Where are the original formulas based on differential calculations that the '56 paper discussed? That is the true Hubbert curve.

Carbonate 23:53, 18 June 2006 (UTC)

There's no such thing. Seriously, go look at the paper. There is no (nontrivial) equation in there.

RandomP 09:22, 19 June 2006 (UTC)

[edit] "Bell shaped", it's not "bell shaped"

(moved from talk:peak oil)

It's the Normal distribution. --Leladax (talk) 09:12, 11 March 2008 (UTC)

They are somewhat similar, and yes they are both bell-shaped. The primary difference is that the Hubbert curve has definite end points, where as the normal distribution never reaches 0 on either side. Compare the formulas at Hubbert curve and normal distribution for more specifics. Did want to see some change in the article? NJGW (talk) 13:25, 11 March 2008 (UTC)
The Hubbert peak graph doesn't reach a 0 at least in the higher end either. Oil is not going to become "0" in production, oil is not going to become "0" in demand either, at least in the long term future. It could be argued that even the beginning of it doesn't start exactly from 0, e.g. cavemen burning it for fire or something in limited quantities. --Leladax (talk) 00:24, 12 March 2008 (UTC)
The normal curve never reaches zero. Ever. One day, man will no longer pump oil. A long time ago (cavemen???, where did you hear that?), man first started pumping oil. Those are zeros on both ends. Also, the normal curve is normally distributed while the Hubbert curve is not. Compare:
Hubbert : x = {e^{-t}\over(1+e^{-t})^2}={1\over2+2\cosh t}
Normal : \varphi(x)=\varphi_{0,1}(x)=\frac{1}{\sqrt{2\pi\,}} \, e^{-\frac{x^2}{2}},\quad x\in\mathbb{R},
The curves do in fact look similar, but they are mathematically different. NJGW (talk) 18:15, 12 March 2008 (UTC)
ok, but I have to point out your "never" is weak, normal distribution reaches zero when x tends to infinity. Also I find your way of thinking on "cavemen" (disregarding the case with such ease) quite simplistic, possibly an attempt to pick a fight, and a drawback in a serious discussion. There's no axiom requiring you thinking of modern oil pumps and be fixed to that. Using oil even by extracting it with buckets or even carrying it in your palms to a cave is still using oil. --Leladax (talk) 19:50, 12 March 2008 (UTC)
Statistically speaking, never is never because infinity never happens. It's only theoretical so I don't know why you'd want to argue with that. I'm sorry you felt I was trying to pick a fight with the caveman thing, but I was just trying to point out that if you cite an example, you really should cite a source for it, or at least point out that you are stating something just for the sake of argument. In either case it doesn't matter because if we assume people first started using oil, we assume there was a beginning, and that implies a zero point one moment before that. As for the other direction, there will be a zero point as well, whether it is when all the oil has been used or when we can't physically pump any more out or when all humans die out. That's the main mathematical difference, though I'm sure a statistician could help us out with the more technical details.
There may also be a time when oil production shoots back up (say for example a new well is discovered, a new technology created, a future environmental pact breached), further moving the curve away from a normal distribution. I guess that that's the practical, and more crucial, reason why Hubberts isn't normally distributed. Either way, what's the point here? Is there something that needs to change in the article? NJGW (talk) 02:45, 13 March 2008 (UTC)
The text reads {cquote| According to the Hubbert model, the production rate of a limited resource will follow a roughly symmetrical bell-shaped curve based on the limits of exploitability and market pressures.}} Is this what Hubbert predicted or not? The article doesn't provide a reference for the statement.LeadSongDog (talk) 03:22, 13 March 2008 (UTC)
I'm pretty sure "bell-shaped" is simply a visual description, though for some reason if you look up bell-shaped on WP, you end up at normal distribution (which I'm not sure is necessarily true, but I'll try to ask a statistitian). This page has a comparison which shows that the Hubbert curve highly resembles a parabola on it's top half, as opposed to a "gauss" curve (normal distribution) on the bottom half. This page however confuses things by suggesting that a normal curve is simply symmetrical (dubious?), but then points out that a real-life Hubbert curve is not symmetrical. NJGW (talk) 04:37, 13 March 2008 (UTC)

(undent) From a stat professor's quick evaluation: "Hubbert function is the derivative of the logistic function so you can always find a normal distribution that will resemble a Hubbert function, and vice versa. The cumulative form of the Hubbert function, though, is more tractable than the cumulative normal. " I'm not really sure what tractable means there, but I think he means you can play around with the numbers a bit more. He's in the middle of getting ready for a big conference or he'd tell me more :( NJGW (talk) 05:21, 13 March 2008 (UTC)