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As the logistic distribution, which can be solved analytically, is similar to the normal distribution, it can be used instead. The blue picture illustrates an example of fitting the logistic distribution to ranked October rainfalls—that are almost normally distributed—and it shows the 90% confidence belt based on the binomial distribution.
Logistic regression is used in various fields, including machine learning, most medical fields, and social sciences. For example, the Trauma and Injury Severity Score (), which is widely used to predict mortality in injured patients, was originally developed by Boyd et al. using logistic regression. [6]
An example of a spider web projection of a trajectory on the graph of the logistic map, and the locations of the fixed points and on the graph. Graphs of maps, especially those of one variable such as the logistic map, are key to understanding the behavior of the map.
The term generalized logistic distribution is used as the name for several different families of probability distributions. For example, Johnson et al. [1] list four forms, which are listed below. Type I has also been called the skew-logistic distribution.
The Linnik distribution; The logistic distribution; The map-Airy distribution; The metalog distribution, which is highly shape-flexible, has simple closed forms, and can be parameterized with data using linear least squares. The normal distribution, also called the Gaussian or the bell curve.
The metalog distribution is a generalization of the logistic distribution, where the term "metalog" is short for "metalogistic".Starting with the logistic quantile function, = = + (), Keelin substituted power series expansions in cumulative probability = for the and the parameters, which control location and scale, respectively.
The Kaniadakis Logistic distribution (also known as κ-Logisticdistribution) is a generalized version of the Logistic distribution associated with the Kaniadakis statistics. It is one example of a Kaniadakis distribution .
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.