Inverse Gamma Distribution is a reciprocal of gamma probability density function with positive shape parameters α,βα,β and location parameter μμ. ααcontrols the height. Higher the αα, taller is the probability density function (PDF). ββ controls the speed. It is defined by following formula.

Formula

f(x)=x−(α+1)e−1βxΓ(α)βαwherex>0f(x)=x−(α+1)e−1βxΓ(α)βαwherex>0

Where −

·        αα = positive shape parameter.

·        ββ = positive shape parameter.

·        xx = random variable.

Following diagram shows the probability density function with different parameter combinations.