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An example J curve. Trade starts in perfect balance, but depreciation at time 0 causes an immediate trade deficit of 50 million dollars. The balance of trade improves over time as consumers react, returning to balance at month 3 and rising to a surplus of 150 million at month 4.
Inverted logistic S-curve to model the relation between wheat yield and soil salinity. Many natural processes, such as those of complex system learning curves, exhibit a progression from small beginnings that accelerates and approaches a climax over time. When a specific mathematical model is lacking, a sigmoid function is often used.
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The standard logistic function is the logistic function with parameters =, =, =, which yields = + = + = / / + /.In practice, due to the nature of the exponential function, it is often sufficient to compute the standard logistic function for over a small range of real numbers, such as a range contained in [−6, +6], as it quickly converges very close to its saturation values of 0 and 1.
The generalized logistic function or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The function is sometimes named Richards's curve after F. J. Richards, who proposed the general form for the family of models in 1959.
The J is steeper on the left hand side, as it is easier for a leader in an authoritarian state to create stability by closing the country than to build a civil society and establish accountable institutions; the curve is higher on the far right than left because states that prevail in opening their societies (Eastern Europe, for example ...
A hockey stick graph or hockey stick curve is a graph, or curve shape, that resembles an ice hockey stick, in that it turns sharply from a nearly flat "blade" to a long "handle". In economics , [ 1 ] [ 2 ] marketing , [ 3 ] and dose–response relationships , [ 4 ] [ 5 ] a hockey stick graph is one in which the "blade" is near zero (hugging the ...
English: The J curve shows the effect of a devaluation of a currency on the net export (exports minus imports). When the devaluation takes place at t the net export falls from A to B, since the level of import is unchanged, but the currency is worth less.