In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. It is closely related to the chi-squared distribution. It is used in Bayesian inference as conjugate prior for the variance of the normal distribution.

Definition

The inverse chi-squared distribution (or inverted-chi-square distribution ) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chi-squared distribution.

degrees of freedom degrees of freedom.

The probability density function of the inverse chi-squared distribution is given by

is the degrees of freedom is the gamma function.

The inverse chi-squared distribution is a special case of the inverse-gamma distribution.

Related distributions

• chi-squared

• scaled-inverse chi-squared

• Inverse gamma

• Inverse chi-squared distribution is a special case of type 5 Pearson distribution

See also

• Scaled-inverse-chi-squared distribution

• Inverse-Wishart distribution

References

External links

• InvChisquare in geoR package for the R Language.