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In mathematics, and in particular, algebra, a generalized inverse (or, g-inverse) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. The purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of ...
The inverse Gaussian and gamma distributions are special cases of the generalized inverse Gaussian distribution for p = −1/2 and b = 0, respectively. [7] Specifically, an inverse Gaussian distribution of the form
Its cumulant generating function (logarithm of the characteristic function) [contradictory] is the inverse of the cumulant generating function of a Gaussian random variable. To indicate that a random variable X is inverse Gaussian-distributed with mean μ and shape parameter λ we write X ∼ IG ( μ , λ ) {\displaystyle X\sim ...
In general, given the probability distribution of a random variable X with strictly positive support, it is possible to find the distribution of the reciprocal, Y = 1 / X. If the distribution of X is continuous with density function f ( x ) and cumulative distribution function F ( x ), then the cumulative distribution function, G ( y ), of the ...
The ginv function calculates a pseudoinverse using the singular value decomposition provided by the svd function in the base R package. An alternative is to employ the pinv function available in the pracma package. The Octave programming language provides a pseudoinverse through the standard package function pinv and the pseudo_inverse() method.
The Fréchet distribution, also known as inverse Weibull distribution, [2] [3] is a special case of the generalized extreme value distribution. It has the cumulative distribution function ( ) = > . where α > 0 is a shape parameter.
Inverse gamma distribution is a special case of type 5 Pearson distribution; A multivariate generalization of the inverse-gamma distribution is the inverse-Wishart distribution. For the distribution of a sum of independent inverted Gamma variables see Witkovsky (2001)
It is characterised by its probability density function, within the support of the distribution, being proportional to the reciprocal of the variable. The reciprocal distribution is an example of an inverse distribution, and the reciprocal (inverse) of a random variable with a reciprocal distribution itself has a reciprocal distribution.