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That definition would be correct only with a symetrical "bell" curve, where mode = median = mean.
More likely, the actual curve is going to be skewed far to the right. In other words, the mode (peak) is far to the left of the median. In other words, it is quite possible for peak production to occur long before we reach the 50% mark. The reason: That 2nd 50% (and actually, quite a bit before that) is much more difficult and costly to get, and thus doesn't come on line at the same pace that the first 50% did.
The curve might be skewed to the left. Humanity might be so addicted to oil that it invests every last dollar in beating the logistic bottleneck and develops every remaining 10 barrel/day puddle simultaneously to keep the economic growth cycle going, followed by catastrophic collapse. Time will tell.
That is an alternative hypothesis, and time will tell. However, the extent of investment in new projects is not presently consistent with your hypothesis. It is more consistent with the hypothesis that as new oil becomes more costly to find and develop, the investments will become fewer and farther between, thus delaying the onset of new flows to < the flows lost to depletion.
Even without some sort of hyper development regime, it is not at all self-evident that the global, all-time production distribution is going to be symmetric around the peak. After all, in the past the world GDP and demand was significantly lower at the same time as big finds were easy. Now we are going to have to shrink demand by force, while no more large fields are available. World population and demand are not going to reverse in the future in a mirror image of the past. More likely is that there will be massive inertia trying to keep the status quo, leading to a catastrophic transition. Who knows, maybe magical new power sources will show up and save the day but until then, oil, gas and coal are going to be exploited (gas and coal will delay the crash).
Normal curves are symmetrical, but Lotka-Volterra (predator-prey) cycles are skewed to the left (crash is faster than growth). It depends on what assumptions you put into the model.
You can include a "effort function" in the D.E. that approximates how the market responds to scarcity. If the effort function is linear($X increase in price of oil always results in $Y increase in investment), there is no change to the shape of the resulting curve; it is still a normal curve, just a bit taller and shifted to the right.
To change the shape will require an "unreasonably aggressive surge in investment".
My technology effect concept is exactly a predator prey relationship. In this case the predator is advancing technology. And the prey is a poor little oil drop. Advancing technology is what transforms a symmetric relationship into a asymmetric one. Noye Moore's law effectively has this form. Eventually it reaches a real physical limit and transistor size no longer shrinks. In my opinion just about every example of refining technology to increase some variable results in a predator prey like relationship.
Thanks for real name for the curve I've been using shark fin.
Still like shark fin though :)