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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 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 Birnbaum–Saunders distribution, also known as the fatigue life distribution, is a probability distribution used extensively in reliability applications to model failure times. The chi distribution. The noncentral chi distribution; The chi-squared distribution, which is the sum of the squares of n independent Gaussian random variables.
Quantile parameterized distributions (QPDs) are convenient for inverse transform sampling in this context. In particular, the Metalog distribution is a flexible continuous probability distribution that has simple closed form equations, can be directly parameterized by data, using only a handful of parameters. [6]
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.
Maximum entropy probability distribution; Maxwell–Boltzmann distribution; McCullagh's parametrization of the Cauchy distributions; Metalog distribution;
A quantile-parameterized distribution (QPD) is a probability distributions that is directly parameterized by data. They were created to meet the need for easy-to-use continuous probability distributions flexible enough to represent a wide range of uncertainties, such as those commonly encountered in business, economics, engineering, and science.
Discrete probability distribution – redirects to section of Probability distribution; Discrete time; ... Metalog distribution; Method of moments (statistics)