The Logistic S-Curve
The logistic function F(x) = 1 / (1 + e-x) was developed to model the growth of a population that multiplies until constrained by exhausted resources. It has the property of exponential growth to the midpoint, followed by exponentially slowing growth.
In my application of the model, the population consists of all speculators who will ever buy bitcoins. That population grows as bitcoin knowledge spreads to new speculators, and that population is eventually limited by the finite number of available speculators. The price series of bitcoin is subject to bubbles and crashes that are ignored by the model, rather the model addresses the price trend.
The S Curve is plotted on my chart using a logarithmic price axis, and thus does not directly resemble the Sigmoid graph above.
The logistic function F(x) = 1 / (1 + e-x) was developed to model the growth of a population that multiplies until constrained by exhausted resources. It has the property of exponential growth to the midpoint, followed by exponentially slowing growth.
In my application of the model, the population consists of all speculators who will ever buy bitcoins. That population grows as bitcoin knowledge spreads to new speculators, and that population is eventually limited by the finite number of available speculators. The price series of bitcoin is subject to bubbles and crashes that are ignored by the model, rather the model addresses the price trend.
The S Curve is plotted on my chart using a logarithmic price axis, and thus does not directly resemble the Sigmoid graph above.