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.
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). The logistic distribution is a special case of the Tukey lambda distribution.
The graph of the logistic map + = is the plane curve that plots the relationship between and +, with (or x) on the horizontal axis and + (or f (x)) on the vertical axis. The graph of the logistic map looks like this, except for the case r = 0:
A graph of the logistic function on the t-interval (−6,6) is shown in Figure 1. Let us assume that t {\displaystyle t} is a linear function of a single explanatory variable x {\displaystyle x} (the case where t {\displaystyle t} is a linear combination of multiple explanatory variables is treated similarly).
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function, which is defined by the formula: [1] = + = + = ().
As shown in the graph on the right, the logit and probit functions are extremely similar when the probit function is scaled, so that its slope at y = 0 matches the slope of the logit. As a result, probit models are sometimes used in place of logit models because for certain applications (e.g., in item response theory) the implementation is ...
A cobweb plot, known also as Lémeray Diagram or Verhulst diagram is a visual tool used in the dynamical systems field of mathematics to investigate the qualitative behaviour of one-dimensional iterated functions, such as the logistic map. The technique was introduced in the 1890s by E.-M. Lémeray. [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.