To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.

Variance-gamma distribution

From Wikipedia, the free encyclopedia

variance-gamma distribution
Parameters location (real)
asymmetry parameter (real)
shape parameter (alternative parameterizations use [1])

denotes a modified Bessel function of the second kind
denotes the Gamma function

The variance-gamma distribution, generalized Laplace distribution[2] or Bessel function distribution[2] is a continuous probability distribution that is defined as the normal variance-mean mixture where the mixing density is the gamma distribution. The tails of the distribution decrease more slowly than the normal distribution. It is therefore suitable to model phenomena where numerically large values are more probable than is the case for the normal distribution. Examples are returns from financial assets and turbulent wind speeds. The distribution was introduced in the financial literature by Madan and Seneta.[3] The variance-gamma distributions form a subclass of the generalised hyperbolic distributions.

The fact that there is a simple expression for the moment generating function implies that simple expressions for all moments are available. The class of variance-gamma distributions is closed under convolution in the following sense. If and are independent random variables that are variance-gamma distributed with the same values of the parameters and , but possibly different values of the other parameters, , and , respectively, then is variance-gamma distributed with parameters , , and .

The variance-gamma distribution can also be expressed in terms of three inputs parameters (C,G,M) denoted after the initials of its founders. If the "C", here, parameter is integer then the distribution has a closed form 2-EPT distribution. See 2-EPT Probability Density Function. Under this restriction closed form option prices can be derived.

If , and , the distribution becomes a Laplace distribution with scale parameter . As long as , alternative choices of and will produce distributions related to the Laplace distribution, with skewness, scale and location depending on the other parameters.[4]

For a symmetric variance-gamma distribution, the kurtosis can be given by .[1]

See also Variance gamma process.

YouTube Encyclopedic

  • 1/5
    1 614
    1 715
  • Mean and Variance of Gamma Distribution Part 3
  • Mean and Variance of Gamma Distribution Part 2
  • Variance-Gamma Distribution
  • Conjugate Prior for Variance of Normal Distribution with known mean
  • The Connection between the Exponential and Gamma Distributions Part 2



  1. ^ a b Nestler, Scott & Hall, Andrew (October 4, 2019). "The variance gamma distribution". The Royal Statistical Society. doi:10.1111/j.1740-9713.2019.01314.x. Retrieved 2020-10-14.CS1 maint: multiple names: authors list (link)
  2. ^ a b Kotz, S.; et al. (2001). The Laplace Distribution and Generalizations. Birkhäuser. p. 180. ISBN 0-8176-4166-1.
  3. ^ D.B. Madan and E. Seneta (1990): The variance gamma (V.G.) model for share market returns, Journal of Business, 63, pp. 511–524.
  4. ^ Meyers, Robert A. (2010). Complex Systems in Finance and Econometrics. Springer. p. 326. ISBN 9781441977007.
This page was last edited on 7 January 2021, at 17:21
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.