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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.
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.
A plant cell wall was first observed and named (simply as a "wall") by Robert Hooke in 1665. [3] However, "the dead excrusion product of the living protoplast" was forgotten, for almost three centuries, being the subject of scientific interest mainly as a resource for industrial processing or in relation to animal or human health.
Ragone plot showing specific energy versus specific power for various energy-storing devices. A Ragone plot (/ r ə ˈ ɡ oʊ n iː / rə-GOH-nee) [1] is a plot used for comparing the energy density of various energy-storing devices.
Bring's curve (genus 4) Macbeath surface (genus 7) Butterfly curve (algebraic) (genus 7) Curve families with variable genus. Polynomial lemniscate; Fermat curve;
The Johnson's S U-distribution is a four-parameter family of probability distributions first investigated by N. L. Johnson in 1949. [ 1 ] [ 2 ] Johnson proposed it as a transformation of the normal distribution : [ 1 ]
While the non-cumulative sales curve with negative q is similar to those with q=0, the cumulative sales curve presents a more interesting situation: When p > -q, the market will reach 100% of its potential, eventually, as for a regular positive value of q. However, if p < -q, at the long-range, the market will saturate at an equilibrium level ...