Inversechisquared distribution
Probability density function  
Cumulative distribution function  
Parameters  

Support  
CDF  
Mean  for 
Mode  
Variance  for 
Skewness  for 
Ex. kurtosis  for 
Entropy 

MGF  ; does not exist as real valued function 
CF 
In probability and statistics, the inversechisquared distribution (or invertedchisquare distribution^{[1]}) is a continuous probability distribution of a positivevalued random variable. It is closely related to the chisquared distribution and its specific importance is that it arises in the application of Bayesian inference to the normal distribution, where it can be used as the prior and posterior distribution for an unknown variance.
Definition
The inversechisquared distribution (or invertedchisquare distribution^{[1]} ) is the probability distribution of a random variable whose multiplicative inverse (reciprocal) has a chisquared distribution. It is also often defined as the distribution of a random variable whose reciprocal divided by its degrees of freedom is a chisquared distribution. That is, if has the chisquared distribution with degrees of freedom, then according to the first definition, has the inversechisquared distribution with degrees of freedom; while according to the second definition, has the inversechisquared distribution with degrees of freedom. Only the first definition will usually be covered in this article.
The first definition yields a probability density function given by
while the second definition yields the density function
In both cases, and is the degrees of freedom parameter. Further, is the gamma function. Both definitions are special cases of the scaledinversechisquared distribution. For the first definition the variance of the distribution is while for the second definition .
Related distributions
 chisquared: If and , then
 scaledinverse chisquared: If , then
 Inverse gamma with and
See also
References
External links
 InvChisquare in geoR package for the R Language.