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The inverse gamma distribution is a right-skew, continuous distribution for a random variables taking positive values.

The inverse gamma distribution is a right-skew, continuous distribution on the positive half of the real line.

It is the distribution of the inverse (reciprocal) of a random variable which is gamma distributed. Explicitly, the density function takes the form:

$$p(x;\alpha,\beta) = \frac{\beta^\alpha}{\Gamma(\alpha)} x^{\alpha-1} \exp \left( -\frac{\beta}{x}\right)$$

It is often used as a prior distribution used in Bayesian statistics. For example, it is a conjugate prior for the variance parameter of a normal distribution.

Reference: Wikipedia on Inverse Gamma