The hyperbolic distribution is a continuous probability distribution characterized by the logarithm of the probability density function being a hyperbola...

probability theory and statistics, the hyperbolic secant distribution is a continuous probability distribution whose probability density function and...

generalised hyperbolic distribution (GH) is a continuous probability distribution defined as the normal variance-mean mixture where the mixing distribution is...

inverse Gaussian distribution. The NIG distribution was noted by Blaesild in 1977 as a subclass of the generalised hyperbolic distribution discovered by...

include the logistic distribution, hyperbolic secant distribution, and the Champernowne distribution. The Laplace distribution is easy to integrate (if...

operations. The log-hyperbolic distribution was proposed by Bagnold and Barndorff-Nielsen to model the particle-size distribution of naturally occurring...

example of a distribution that has a finite expected value but infinite variance. The hyperbolic distribution The hyperbolic secant distribution The Johnson...

Springer-Verlag 2012 Generalised hyperbolic distribution Generalized inverse Gaussian distribution Hyperbolic distribution Information geometry List of mathematicians...

variance-gamma distribution, which in turn is a special case of generalised hyperbolic distribution. A simpler special case of the generalized K-distribution is often...

\gamma )} . The Cauchy distribution is a singular limit of a hyperbolic distribution[citation needed] The wrapped Cauchy distribution, taking values on a...

common use: inverse hyperbolic sine, inverse hyperbolic cosine, inverse hyperbolic tangent, inverse hyperbolic cosecant, inverse hyperbolic secant, and inverse...

In statistics, a symmetric probability distribution is a probability distribution—an assignment of probabilities to possible occurrences—which is unchanged...

mixtures is the generalised hyperbolic distribution in which the mixing distribution is the generalized inverse Gaussian distribution. The probability density...

logistic functions. The cumulative distribution function of the logistic distribution is also a scaled version of the hyperbolic tangent. F ( x ; μ , s ) = 1...

(2021). "On bounds for the mode and median of the generalized hyperbolic and related distributions". Journal of Mathematical Analysis and Applications. 493...

In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis...

Madan and Seneta. The variance-gamma distributions form a subclass of the generalised hyperbolic distributions. The fact that there is a simple expression...

Hyper-exponential distribution Hyper-Graeco-Latin square design Hyperbolic distribution Hyperbolic secant distribution Hypergeometric distribution Hyperparameter...

A hyperbolic geometric graph (HGG) or hyperbolic geometric network (HGN) is a special type of spatial network where (1) latent coordinates of nodes are...

oldest and most universal laws – every community shows a hollow curve or hyperbolic shape on a histogram with many rare species and just a few common species...

Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical...

statistics, the multivariate normal distribution, multivariate Gaussian distribution, or joint normal distribution is a generalization of the one-dimensional...

hyperbolic secant distribution, orange curve, excess kurtosis = 2 L: logistic distribution, green curve, excess kurtosis = 1.2 N: normal distribution...

Symmetric multivariate Laplace distribution Multivariate logistic distribution Multivariate symmetric general hyperbolic distribution In the 2-dimensional case...

Scientific. Amanda Folsom Árpád Tóth Jack Buttcane Duke, W. (1988) Hyperbolic distribution problems and half-integral weight Maass forms, Inventiones Mathematicae...

to 1. A wide variety of sigmoid functions including the logistic and hyperbolic tangent functions have been used as the activation function of artificial...

noncentral chi-squared distribution (or noncentral chi-square distribution, noncentral χ 2 {\displaystyle \chi ^{2}} distribution) is a noncentral generalization...

heterogeneous degree distribution then simply reflects the negative curvature and metric properties of the underlying hyperbolic geometry. Starting with...

\mathrm {FWHM} =2\gamma .} Another important distribution function, related to solitons in optics, is the hyperbolic secant: f ( x ) = sech ⁡ ( x X ) . {\displaystyle...

logistic function into the logistic distribution. Geometrically, the hyperbolic tangent function is the hyperbolic angle on the unit hyperbola x 2 − y...