Search results
Results from the WOW.Com Content Network
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.
Asymptotically, bounded growth approaches a fixed value. This contrasts with exponential growth, which is constantly increasing at an accelerating rate, and therefore approaches infinity in the limit. Examples of bounded growth include the logistic function, the Gompertz function, and a simple modified exponential function like y = a + be gx. [1]
Although growth may initially be exponential, the modelled phenomena will eventually enter a region in which previously ignored negative feedback factors become significant (leading to a logistic growth model) or other underlying assumptions of the exponential growth model, such as continuity or instantaneous feedback, break down.
In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis).
By now, it is a widely accepted view to analogize Malthusian growth in Ecology to Newton's First Law of uniform motion in physics. [8] Malthus wrote that all life forms, including humans, have a propensity to exponential population growth when resources are abundant but that actual growth is limited by available resources:
The logistic function can be calculated efficiently by utilizing type III Unums. [ 8 ] An hierarchy of sigmoid growth models with increasing complexity (number of parameters) was built [ 9 ] with the primary goal to re-analyze kinetic data, the so called N-t curves, from heterogeneous nucleation experiments, [ 10 ] in electrochemistry .
Mathematically, the basic Bass diffusion is a Riccati equation with constant coefficients equivalent to Verhulst—Pearl logistic growth. In 1969, Frank Bass published his paper on a new product growth model for consumer durables .
In logistic populations however, the intrinsic growth rate, also known as intrinsic rate of increase (r) is the relevant growth constant. Since generations of reproduction in a geometric population do not overlap (e.g. reproduce once a year) but do in an exponential population, geometric and exponential populations are usually considered to be ...