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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)
The closely related inverse-gamma distribution is used as a conjugate prior for scale parameters, such as the variance of a normal distribution. If α is a positive integer, then the distribution represents an Erlang distribution; i.e., the sum of α independent exponentially distributed random variables, each of which has a mean of θ.
The Inverse Wishart distribution is a special case of the inverse matrix gamma distribution when the shape parameter = and the scale parameter =. Another generalization has been termed the generalized inverse Wishart distribution, G W − 1 {\displaystyle {\mathcal {GW}}^{-1}} .
Download QR code; Print/export ... an inverse distribution is the distribution of the reciprocal of a random variable. ... inverse-gamma distribution
In probability theory and statistics, the normal-inverse-gamma distribution (or Gaussian-inverse-gamma distribution) is a four-parameter family of multivariate continuous probability distributions. It is the conjugate prior of a normal distribution with unknown mean and variance .
The Gamma distribution, which describes the time until n consecutive rare random events occur in a process with no memory. The Erlang distribution, which is a special case of the gamma distribution with integral shape parameter, developed to predict waiting times in queuing systems; The inverse-gamma distribution; The generalized gamma distribution
In probability theory and statistics, the Lévy distribution, named after Paul Lévy, is a continuous probability distribution for a non-negative random variable. In spectroscopy, this distribution, with frequency as the dependent variable, is known as a van der Waals profile. [note 1] It is a special case of the inverse-gamma distribution.
Examples [ edit ] Many very common probability distributions belong to the class of EDMs, among them are: normal distribution , binomial distribution , Poisson distribution , negative binomial distribution , gamma distribution , inverse Gaussian distribution , and Tweedie distribution .