Name for several different families of probability distributions
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. Type IV subsumes the other types and is obtained when applying the logit transform to beta random variates. Following the same convention as for the log-normal distribution, type IV may be referred to as the logistic-beta distribution, with reference to the standard logistic function, which is the inverse of the logit transform.
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.
^Johnson, N.L., Kotz, S., Balakrishnan, N. (1995) Continuous Univariate Distributions, Volume 2, Wiley. ISBN 0-471-58494-0 (pages 140–142)
and 25 Related for: Generalized logistic distribution information
The term generalizedlogisticdistribution is used as the name for several different families of probability distributions. For example, Johnson et al...
statistics, the logisticdistribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears...
variables. The generalizedlogisticdistribution The generalized normal distribution The geometric stable distribution The Gumbel distribution The Holtsmark...
log-odds or logistic model. Generalized linear models cover all these situations by allowing for response variables that have arbitrary distributions (rather...
'(\alpha ,\beta )} , then ln X {\displaystyle \ln X} has a generalizedlogisticdistribution. More generally, if X ∼ β ′ ( α , β , p , q ) {\displaystyle...
A logistic function or logistic curve is a common S-shaped curve (sigmoid curve) with the equation f ( x ) = L 1 + e − k ( x − x 0 ) {\displaystyle f(x)={\frac...
binary logistic regression generalized to multinomial logistic regression. If the multiple categories are ordered, one can use the ordinal logistic regression...
The symmetric generalized normal distribution, also known as the exponential power distribution or the generalized error distribution, is a parametric...
In statistics, multinomial logistic regression is a classification method that generalizeslogistic regression to multiclass problems, i.e. with more than...
The Kaniadakis Logisticdistribution (also known as κ-Logisticdistribution) is a generalized version of the Logisticdistribution associated with the Kaniadakis...
theory and statistics, the generalized extreme value (GEV) distribution is a family of continuous probability distributions developed within extreme value...
log X 1 − X {\displaystyle Y=\log {\frac {X}{1-X}}} has a generalizedlogisticdistribution, with density σ ( y ) α σ ( − y ) β B ( α , β ) {\displaystyle...
statistics, the Gumbel distribution (also known as the type-I generalized extreme value distribution) is used to model the distribution of the maximum (or...
Gaussian distributionGeneralized least squares Generalized linear array model Generalized linear mixed model Generalized linear model Generalizedlogistic distribution...
}[1+(x/x_{0})^{\alpha }]^{2}}},\qquad x>0.} Generalizedlogisticdistribution C. Kleiber and S. Kotz (2003). Statistical Size Distributions in Economics and Actuarial...
elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively...
Singh–Maddala distribution and is one of a number of different distributions sometimes called the "generalized log-logisticdistribution". The Burr (Type...
Cauchy, Student's t, and logisticdistributions). For other names, see Naming. The univariate probability distribution is generalized for vectors in the multivariate...
The exponential generalized beta (EGB) distribution follows directly from the GB and generalizes other common distributions. A generalized beta random variable...
function is the quantile function associated with the standard logisticdistribution. It has many uses in data analysis and machine learning, especially...
and statistics, the skewed generalized "t" distribution is a family of continuous probability distributions. The distribution was first introduced by Panayiotis...
follow a multivariate normal distribution. If the errors do not follow a multivariate normal distribution, generalized linear models may be used to relax...
mode include the logisticdistribution, hyperbolic secant distribution, and the Champernowne distribution. The Laplace distribution is easy to integrate...
{\Sigma }}} , also known as the generalized variance. The equation above reduces to that of the univariate normal distribution if Σ {\displaystyle {\boldsymbol...
Global Information