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The metalog distribution is generalization of the logistic distribution, in which power series expansions in terms of are substituted for logistic parameters and . The resulting metalog quantile function is highly shape flexible, has a simple closed form, and can be fit to data with linear least squares.
The survival distribution function of κ-Logistic distribution is given by = +valid for .The survival Logistic distribution is recovered in the classical limit .. The hazard function associated with the κ-Logistic distribution is obtained by the solution of the following evolution equation:
For other families of distributions that have also been called generalized logistic distributions, see the shifted log-logistic distribution, which is a generalization of the log-logistic distribution; and the metalog ("meta-logistic") distribution, which is highly shape-and-bounds flexible and can be fit to data with linear least squares.
Logistics engineering is a complex science that considers trade-offs in component/system design, repair capability, training, spares inventory, demand history, storage and distribution points, transportation methods, etc., to ensure the "thing" is where it's needed, when it's needed, and operating the way it's needed all at an acceptable cost.
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.
It is a symmetric logistic distribution curve, [1] often confused with the "normal" gaussian function. It first appeared in "Nuclear Energy and the Fossil Fuels," geologist M. King Hubbert's 1956 presentation to the American Petroleum Institute, as an idealized symmetric curve, during his tenure at the Shell Oil Company. [1]
Another generalized log-logistic distribution is the log-transform of the metalog distribution, in which power series expansions in terms of are substituted for logistic distribution parameters and . The resulting log-metalog distribution is highly shape flexible, has simple closed form PDF and quantile function , can be fit to data with linear ...
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.